<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                            ------------------------

                                    FORM 10-Q

(MARK ONE)

[x]       QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
          EXCHANGE ACT OF 1934

For the quarterly period ended     June 30, 1998
                               ---------------------

                                       OR

[ ]       TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
          EXCHANGE ACT OF 1934

For the transition period from ____________________ to ____________________

                         Commission File Number   0-18495
                                                 ---------

                    Enstar Income/Growth Program Six-B, L.P.
--------------------------------------------------------------------------------
             (Exact name of Registrant as specified in its charter)

          Georgia                                               58-1754588
-------------------------------                           ----------------------
(State or other jurisdiction of                              (I.R.S. Employer 
incorporation or organization)                            Identification Number)

10900 Wilshire Boulevard - 15th Floor
      Los Angeles, California                                     90024
----------------------------------------                  ----------------------
(Address of principal executive offices)                        (Zip Code)

Registrant's telephone number, including area code: (310) 824-9990
                                                   -----------------


--------------------------------------------------------------------------------
              Former name, former address and former fiscal year,
                         if changed since last report.



          Indicate by check mark whether the registrant (1) has filed all
reports required to be filed by Section 13 or 15(d) of the Securities Exchange
Act of 1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. Yes  X   No 
                                             -----   ----- 

                       Exhibit Index located at Page E-1.


<PAGE>   2
                         PART I - FINANCIAL INFORMATION

                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                            CONDENSED BALANCE SHEETS

                  ===========================================


<TABLE>
<CAPTION>
                                                                        December 31,           June 30,
                                                                           1997*                 1998
                                                                        -----------           -----------
                                                                                              (Unaudited)
<S>                                                                     <C>                   <C>        
ASSETS:
  Cash and cash equivalents                                             $   304,800           $   519,100
                                                                                           
  Accounts receivable, less allowance of $2,500 and                                        
     $2,400 for possible losses                                             101,500                72,700
                                                                                           
  Prepaid expenses and other assets                                          48,800                55,500
                                                                                           
  Property, plant and equipment, less accumulated                                          
     depreciation and amortization of $3,244,600 and $3,581,900           3,477,400             3,427,500
                                                                                           
  Franchise cost, net of accumulated                                                       
     amortization of $2,615,600 and $2,796,100                            1,714,100             1,539,300
                                                                                           
  Intangible costs, net of accumulated amortization                                        
     of $380,800 and $383,400                                               248,100               219,400
                                                                        -----------           -----------
                                                                                           
                                                                        $ 5,894,700           $ 5,833,500
                                                                        ===========           ===========
                                                                                           
                                     LIABILITIES AND PARTNERSHIP CAPITAL                                 
                                     -----------------------------------                                 
LIABILITIES:                                                                               
  Accounts payable                                                      $   176,500           $   196,300
  Due to affiliates                                                         430,300               464,900
  Note payable - affiliate                                                1,750,000             1,600,000
                                                                        -----------           -----------
                                                                                           
         TOTAL LIABILITIES                                                2,356,800             2,261,200
                                                                        -----------           -----------
                                                                                           
COMMITMENTS AND CONTINGENCIES                                                              
                                                                                           
PARTNERSHIP CAPITAL (DEFICIT):                                                             
  General partners                                                          (37,300)              (37,000)
  Limited partners                                                        3,575,200             3,609,300
                                                                        -----------           -----------
                                                                                           
         TOTAL PARTNERSHIP CAPITAL                                        3,537,900             3,572,300
                                                                        -----------           -----------
                                                                                           
                                                                        $ 5,894,700           $ 5,833,500
                                                                        ===========           ===========
</TABLE>


               *As presented in the audited financial statements.
            See accompanying notes to condensed financial statements.


                                      -2-


<PAGE>   3
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                       CONDENSED STATEMENTS OF OPERATIONS

                  ===========================================


<TABLE>
<CAPTION>
                                                             Unaudited
                                                 ---------------------------------
                                                        Three months ended
                                                             June 30,
                                                 ---------------------------------
                                                   1997                1998
                                                 -----------           -----------
<S>                                              <C>                   <C>        
REVENUES                                         $   727,100           $   768,100
                                                                  
OPERATING EXPENSES:                                               
  Service costs                                      243,300               251,300
  General and administrative expenses                101,900               112,600
  General Partner management fees                                 
     and reimbursed expenses                          68,100                71,000
  Depreciation and amortization                      275,900               281,700
                                                 -----------           -----------
                                                                  
                                                     689,200               716,600
                                                 -----------           -----------
                                                                  
OPERATING INCOME                                      37,900                51,500
                                                 -----------           -----------
                                                                  
OTHER INCOME (EXPENSE):                                           
  Interest income                                      2,100                 5,000
  Interest expense                                   (31,400)              (40,500)
  Gain on sale of cable assets                            --                   900
                                                 -----------           -----------
                                                                  
                                                     (29,300)              (34,600)
                                                 -----------           -----------
                                                                  
NET INCOME                                       $     8,600           $    16,900
                                                 ===========           ===========
                                                                  
Net income allocated to General Partners         $       100           $       200
                                                 ===========           ===========
                                                                  
Net income allocated to Limited Partners         $     8,500           $    16,700
                                                 ===========           ===========
                                                                  
NET INCOME PER UNIT OF LIMITED                                    
   PARTNERSHIP INTEREST                          $      0.23           $      0.46
                                                 ===========           ===========
                                                                  
AVERAGE LIMITED PARTNERSHIP                                       
   UNITS OUTSTANDING DURING PERIOD                    36,626                36,626
                                                 ===========           ===========
</TABLE>


            See accompanying notes to condensed financial statements.


                                      -3-


<PAGE>   4
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                       CONDENSED STATEMENTS OF OPERATIONS

                  ===========================================


<TABLE>
<CAPTION>
                                                             Unaudited
                                                 ---------------------------------
                                                           Six months ended
                                                              June 30,
                                                 ---------------------------------
                                                    1997                  1998
                                                 -----------           -----------
<S>                                              <C>                   <C>        
REVENUES                                         $ 1,457,900           $ 1,521,700
                                                 -----------           -----------
                                                               
OPERATING EXPENSES:                                            
  Service costs                                      483,400               510,400
  General and administrative expenses                202,000               211,700
  General Partner management fees                              
     and reimbursed expenses                         134,400               138,500
  Depreciation and amortization                      547,100               554,100
                                                 -----------           -----------
                                                               
                                                   1,366,900             1,414,700
                                                 -----------           -----------
                                                               
OPERATING INCOME                                      91,000               107,000
                                                 -----------           -----------
                                                               
OTHER INCOME (EXPENSE):                                        
  Interest income                                      4,200                 8,100
  Interest expense                                   (64,500)              (81,600)
  Gain on sale of cable assets                            --                   900
                                                 -----------           -----------
                                                               
                                                     (60,300)              (72,600)
                                                 -----------           -----------
                                                               
NET INCOME                                       $    30,700           $    34,400
                                                 ===========           ===========
                                                               
Net income allocated to General Partners         $       300           $       300
                                                 ===========           ===========
                                                               
Net income allocated to Limited Partners         $    30,400           $    34,100
                                                 ===========           ===========
                                                               
NET INCOME PER UNIT OF LIMITED                                 
   PARTNERSHIP INTEREST                          $      0.83           $      0.93
                                                 ===========           ===========
                                                               
AVERAGE LIMITED PARTNERSHIP                                    
   UNITS OUTSTANDING DURING PERIOD                    36,626                36,626
                                                 ===========           ===========
</TABLE>


            See accompanying notes to condensed financial statements.


                                      -4-


<PAGE>   5
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                            STATEMENTS OF CASH FLOWS

                  ===========================================


<TABLE>
<CAPTION>
                                                                         Unaudited
                                                              ------------------------------
                                                                    Six months ended
                                                                        June 30,
                                                              ------------------------------
                                                                  1997              1998
                                                              -----------        -----------
<S>                                                           <C>                <C>        
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net income                                                  $    30,700        $    34,400
  Adjustments to reconcile net income to net cash
     provided by operating activities:
      Depreciation and amortization                               547,100            554,100
      Amortization of deferred loan costs                             900              3,900
      Gain on sale of cable assets                                     --               (900)
      Increase (decrease) from changes in:
        Receivables                                               241,500             28,800
        Prepaid expenses and other assets                            (500)            (6,700)
        Accounts payable                                           16,800             19,800
                                                              -----------        -----------

          Net cash provided by operating activities               836,500            633,400
                                                              -----------        -----------

CASH FLOWS FROM INVESTING ACTIVITIES:
  Capital expenditures                                           (272,900)          (294,000)
  Increase in intangible assets                                    (1,900)            (9,300)
  Proceeds from sale of property, plant and equipment                  --                900
                                                              -----------        -----------

          Net cash used in investing activities                  (274,800)          (302,400)
                                                              -----------        -----------

CASH FLOWS FROM FINANCING ACTIVITIES:
  Due to affiliates                                              (446,500)            34,600
  Repayment of debt                                              (211,300)          (150,000)
  Deferred loan costs                                                  --             (1,300)
                                                              -----------        -----------

          Net cash used in financing activities                  (657,800)          (116,700)
                                                              -----------        -----------

INCREASE (DECREASE) IN CASH AND
   CASH EQUIVALENTS                                               (96,100)           214,300

CASH AND CASH EQUIVALENTS
   AT BEGINNING OF PERIOD                                         353,500            304,800
                                                              -----------        -----------

CASH AND CASH EQUIVALENTS
   AT END OF PERIOD                                           $   257,400        $   519,100
                                                              ===========        ===========
</TABLE>


            See accompanying notes to condensed financial statements.


                                      -5-


<PAGE>   6
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                     NOTES TO CONDENSED FINANCIAL STATEMENTS

                     =======================================


1.        INTERIM FINANCIAL STATEMENTS

          The accompanying condensed interim financial statements for the three
and six months ended June 30, 1998 and 1997 are unaudited. These condensed
interim financial statements should be read in conjunction with the audited
financial statements and notes thereto included in the Partnership's latest
Annual Report on Form 10-K. In the opinion of management, such statements
reflect all adjustments (consisting only of normal recurring adjustments)
necessary for a fair presentation of the results of such periods. The results of
operations for the three and six months ended June 30, 1998 are not necessarily
indicative of results for the entire year.

2.        TRANSACTIONS WITH THE GENERAL PARTNERS AND AFFILIATES

        The Partnership has a management and service agreement with a wholly
owned subsidiary of the Corporate General Partner (the "Manager") for a monthly
management fee of 5% of revenues, excluding revenues from the sale of cable
television systems or franchises. Management fee expense approximated $38,400
and $76,100 for the three and six months ended June 30, 1998.

        In addition to the monthly management fee described above, the
Partnership reimburses the Manager for direct expenses incurred on behalf of the
Partnership and for the Partnership's allocable share of operational costs
associated with services provided by the Manager. All cable television
properties managed by the Corporate General Partner and its subsidiary are
charged a proportionate share of these expenses. The Corporate General Partner
has contracted with Falcon Holding Group, L.P. ("FHGLP"), an affiliated
partnership, to provide corporate management services for the Partnership.
Corporate office allocations and district office expenses are charged to the
properties served based primarily on the respective percentage of basic
subscribers or homes passed (dwelling units within a system) within the
designated service areas. The total amount charged to the Partnership for these
services approximated $32,600 and $62,400 for the three and six months ended
June 30, 1998. The payment of management fees and reimbursed expenses was
deferred in prior years. On September 30, 1997, the Partnership obtained new
financing and subsequently used such borrowings and other available cash to pay
$387,500 of its previously deferred management fees and reimbursed expenses,
which approximated $632,100. The remainder of these deferred amounts, $244,600,
was contributed as an equity contribution by the Corporate General Partner to
its subsidiary, Enstar Finance Company, LLC ("EFC"), and remains an outstanding
obligation of the Partnership. In the normal course of business, the Partnership
pays interest and principal to EFC, its primary lender.

        The Partnership also receives certain system operating management
services from affiliates of the Corporate General Partner in addition to the
Manager due to the fact that there are no employees directly employed by the
Partnership. The Partnership reimburses the affiliates for its allocable share
of the affiliates' operational costs. The total amount charged to the
Partnership for these costs approximated $71,700 and $137,800 for the three and
six months ended June 30, 1998. No management fee is payable to the affiliates
by the Partnership and there is no duplication of reimbursed expenses and costs
paid to the Manager.


                                      -6-


<PAGE>   7
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                     NOTES TO CONDENSED FINANCIAL STATEMENTS

                     =======================================

2.      TRANSACTIONS WITH THE GENERAL PARTNERS AND AFFILIATES (CONTINUED)

        Certain programming services have been purchased through an affiliate of
the Partnership. In turn, the affiliate charges the Partnership for these costs
based on an estimate of what the Corporate General Partner could negotiate for
such programming services for the 15 partnerships managed by the Corporate
General Partner as a group. The Partnership recorded programming fee expense of
$149,700 and $296,400 for the three and six months ended June 30, 1998.
Programming fees are included in service costs in the statements of operations.

3.      SALE OF PARTNERSHIP ASSETS

        As reported in the Partnership's Quarterly Report on Form 10-Q for the
quarter ended March 31, 1998, the Partnership concluded that it is not able to
obtain the appropriate amount of capital to make the necessary upgrades to its
cable systems and initiated discussions with a business broker to sell the
Partnership's cable systems. The Partnership subsequently engaged a business
broker to solicit offers for its cable systems, but received only two
preliminary offers (the "Initial Offers"), each of which excluded the Ivins,
Utah and Fisk, Missouri cable systems and was subject to multiple potential
purchase price adjustments and material closing contingencies. The Partnership
concluded that it was not in the best interests of unitholders to accept either
of the Initial Offers because, among other things, neither Initial Offer
constituted an offer to purchase all of the cable systems, and each Initial
Offer was subject to material terms and conditions prior to closing. Subsequent
to the Partnership's receipt of the Initial Offers, the Partnership received an
offer from certain affiliates of FHGLP (the "Purchasers") to purchase all of the
Partnership's cable systems for $10,473,200, a price which exceeded the highest
of the Initial Offers, and which contained only limited closing conditions that
are more favorable to the Partnership than those in the Initial Offers.

        The General Partner believes that accepting the Falcon Offer is in the
best interests of the Partnership and the unitholders. Accordingly, the
Partnership and the Purchasers are in the process of finalizing an asset
purchase agreement for the purchase and sale of all of the Partnership's assets,
subject to limited partner approval as discussed below. If the sale is
consummated, the General Partner will make one or more liquidating distributions
to the partners and, after providing for the payment of the Partnership's
obligations, cause the Partnership to dissolve and be liquidated. After
repayment of the Partnership's existing obligations, the Partnership presently
estimates that liquidating distributions to unitholders would total between $220
and $230 per unit, less applicable taxes, if any. The sale will require the
holders of at least a majority of the Partnership's limited partnership units to
consent to the sale, to certain amendments to the Partnership's partnership
agreement and to the liquidation.


                                      -7-


<PAGE>   8
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                     NOTES TO CONDENSED FINANCIAL STATEMENTS

                     =======================================

4.        EARNINGS PER UNIT OF LIMITED PARTNERSHIP INTEREST

          Earnings and losses per unit of limited partnership interest is based
on the average number of units outstanding during the periods presented. For
this purpose, earnings and losses have been allocated 99% to the Limited
Partners and 1% to the General Partners. The General Partners do not own units
of partnership interest in the Partnership, but rather hold a participation
interest in the income, losses and distributions of the Partnership.


                                      -8-


<PAGE>   9
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.


ITEM 2.    MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
           RESULTS OF OPERATIONS

INTRODUCTION

          The Cable Television Consumer Protection and Competition Act of 1992
(the "1992 Cable Act") required the Federal Communications Commission ("FCC")
to, among other things, implement extensive regulation of the rates charged by
cable television systems for basic and programming service tiers, installation,
and customer premises equipment leasing. Compliance with those rate regulations
has had a negative impact on the Partnership's revenues and cash flow. The
Telecommunications Act of 1996 (the "1996 Telecom Act") substantially changed
the competitive and regulatory environment for cable television and
telecommunications service providers. Among other changes, the 1996 Telecom Act
provides that the regulation of cable programming service tier ("CPST") rates
will be terminated on March 31, 1999. Because cable service rate increases have
continued to outpace inflation under the FCC's existing regulations, the
Partnership expects Congress and the FCC to explore additional methods of
regulating cable service rate increases, including deferral or repeal of the
March 31, 1999 termination of CPST rate regulation. There can be no assurance as
to what, if any, further action may be taken by the FCC, Congress or any other
regulatory authority or court, or the effect thereof on the Partnership's
business. Accordingly, the Partnership's historical financial results as
described below are not necessarily indicative of future performance.

          This Report includes certain forward looking statements regarding,
among other things, future results of operations, regulatory requirements,
competition, capital needs and general business conditions applicable to the
Partnership. Such forward looking statements involve risks and uncertainties
including, without limitation, the uncertainty of legislative and regulatory
changes and the rapid developments in the competitive environment facing cable
television operators such as the Partnership. In addition to the information
provided herein, reference is made to the Partnership's Annual Report on Form
10-K for the year ended December 31, 1997 for additional information regarding
such matters and the effect thereof on the Partnership's business.

RESULTS OF OPERATIONS

          The Partnership's revenues increased from $727,100 to $768,100, or by
5.6%, and from $1,457,900 to $1,521,700, or by 4.4%, for the three and six
months ended June 30, 1998 as compared to the corresponding periods in 1997. Of
the $41,000 increase in revenues for the three months ended June 30, 1998 as
compared to the corresponding period in 1997, $23,800 was due to increases in
regulated service rates that were implemented by the Partnership in 1997 and
$17,200 was due to increases in the number of subscriptions for basic, premium
and tier services. Of the $63,800 increase in revenues for the six months ended
June 30, 1998 as compared to the corresponding period in 1997, $44,400 was due
to increases in regulated service rates that were implemented by the Partnership
in 1997 and $26,200 was due to increases in the number of subscriptions for
basic, premium and tier services. These increases were partially offset by a
decrease of $6,800 in other revenue producing items such as advertising sales
revenue. As of June 30, 1998, the Partnership had approximately 7,400 basic
subscribers and 1,800 premium service units.

          Service costs increased from $243,300 to $251,300, or by 3.3%, and
from $483,400 to $510,400, or by 5.6%, for the three and six months ended June
30, 1998 as compared to the corresponding periods in 1997.


                                      -9-


<PAGE>   10
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

RESULTS OF OPERATIONS (CONTINUED)

Service costs represent costs directly attributable to providing cable services
to customers. The increases were primarily due to increases in programming fees
resulting from higher rates charged by program suppliers.

          General and administrative expenses increased from $101,900 to
$112,600, or by 10.5%, and from $202,000 to $211,700, or by 4.8%, for the three
and six months ended June 30, 1998 as compared to the corresponding periods in
1997. The increases were primarily due to higher professional fees, including
audit expense and investor services costs.

          Management fees and reimbursed expenses increased from $68,100 to
$71,000, or by 4.3%, and from $134,400 to $138,500, or by 3.1%, for the three
and six months ended June 30, 1998 as compared to the corresponding periods in
1997. Management fees increased in direct relation to increased revenues as
described above. Reimbursed expenses remained relatively unchanged.

          Depreciation and amortization expense increased from $275,900 to
$281,700, or by 2.1%, and from $547,100 to $554,100, or by 1.3%, for the three
and six months ended June 30, 1998 as compared to the corresponding periods in
1997. The increases were due to asset additions related to the upgrade and
extension of the Partnership's plant.

          Operating income increased from $37,900 to $51,500, or by 35.9%, and
from $91,000 to $107,000, or by 17.6%, for the three and six months ended June
30, 1998 as compared to the corresponding periods in 1997. The increases were
primarily due to increases in revenues as described above.

          Interest income increased from $2,100 to $5,000 and by $4,200 to
$8,100 for the three and six months ended June 30, 1998 as compared to the
corresponding periods in 1997. The increases were primarily due to higher
average cash balances available for investment in the 1998 periods as compared
to the corresponding periods in 1997.

          Interest expense increased from $31,400 to $40,500, or by 29.0%, and
from $64,500 to $81,600, or by 26.5%, for the three and six months ended June
30, 1998 as compared to the corresponding periods in 1997. The increases were
primarily due to increases in average borrowings in the three and six months
ended June 30, 1998 as compared to the corresponding periods in 1997.

          Due to the factors described above, the Partnership's net income
increased from $8,600 to $16,900, or by 96.5%, and from $30,700 to $34,400, or
by 12.1%, for the three and six months ended June 30, 1998 as compared to the
corresponding periods in 1997.

          Based on its experience in the cable television industry, the
Partnership believes that operating income before depreciation and amortization
(EBITDA) and related measures of cash flow serve as important financial analysis
tools for measuring and comparing cable television companies in several areas,
such as liquidity, operating performance and leverage. EBITDA is not a
measurement determined under generally accepted accounting principles ("GAAP")
and does not represent cash generated from operating activities in accordance
with GAAP. EBITDA should not be considered by the reader as an alternative to
net income as an indicator of financial performance or as an alternative to cash
flows as a measure of liquidity.


                                      -10-


<PAGE>   11
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

RESULTS OF OPERATIONS (CONTINUED)

In addition, the definition of EBITDA may not be identical to similarly titled
measures used by other companies. EBITDA as a percentage of revenues increased
from 43.2% to 43.4% and decreased from 43.8% to 43.4% during the three and six
months ended June 30, 1998 compared to the corresponding periods in 1997. The
three months' increase was due to higher revenues. The decrease for the six
months was primarily due to higher programming fees. EBITDA increased from
$313,800 to $333,200, or by 6.2%, and from $638,100 to $661,100, or by 3.6%,
during the three and six months ended June 30, 1998 as compared to the
corresponding periods in 1997.

LIQUIDITY AND CAPITAL RESOURCES

          The Partnership's primary objective, having invested its net offering
proceeds in cable systems, is to distribute to its partners all available cash
flow from operations and proceeds from the sale of cable systems, if any, after
providing for expenses, debt service and capital requirements relating to the
expansion, improvement and upgrade of its cable systems.

          As of the date of this Report, substantially all of the available
channel capacity in the Partnership's systems is being utilized and each of such
systems requires upgrading. The desired upgrade program is presently estimated
to require aggregate capital expenditures of approximately $7.5 million. These
upgrades cover seven franchise areas in Georgia and are currently required in
three existing franchise agreements. The cost to upgrade the three franchise
areas is estimated to be approximately $2.9 million and must be completed by
February and May 1999, respectively. Two of the remaining four franchise
agreements are under negotiation for renewal.

          The Partnership has insufficient borrowing capacity remaining under
the Facility (as defined below) and would require additional sources of capital
to undertake its upgrade program. The partnership agreement, however, contains
certain limitations on the Partnership's indebtedness. The partnership agreement
provides that without the approval of the holders of a majority of the
Partnership's limited partnership units, the Partnership may not incur any
borrowings unless the amount of such borrowings together with all outstanding
borrowings does not exceed 33% of the original capital raised by the
Partnership, or a maximum of $3,052,500 permitted debt outstanding. In order to
obtain the appropriate amount of capital to upgrade the Partnership's systems as
discussed above, this provision of the partnership agreement would need to be
amended to increase the Partnership's leverage. The Partnership does not intend
to seek such an amendment to the partnership agreement. As reported in the
Partnership's Quarterly Report on Form 10-Q for the quarter ended March 31,
1998, the Partnership concluded that it is not able to obtain the appropriate
amount of capital to make the necessary upgrades to its cable systems and
initiated discussions with a business broker to sell the Partnership's cable
systems. The Partnership subsequently engaged a business broker to solicit
offers for its cable systems, but received only two preliminary offers (the
"Initial Offers"), each of which excluded the Ivins, Utah and Fisk, Missouri
cable systems and was subject to multiple potential purchase price adjustments
and material closing contingencies. The Partnership concluded that it was not in
the best interests of unitholders to accept either of the Initial Offers
because, among other things, neither Initial Offer constituted an offer to
purchase all of the cable systems, and each Initial Offer was subject to
material terms and conditions prior to closing. Subsequent to the Partnership's
receipt of the Initial Offers, the Partnership received an offer from certain
affiliates of FHGLP (the "Purchasers") to


                                      -11-


<PAGE>   12
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

LIQUIDITY AND CAPITAL RESOURCES (CONTINUED)

purchase all of the Partnership's cable systems for $10,473,200, a price which
exceeded the highest of the Initial Offers, and which contained only limited
closing conditions that are more favorable to the Partnership than those in the
Initial Offers.

        The General Partner believes that accepting the Falcon Offer is in the
best interests of the Partnership and the unitholders. Accordingly, the
Partnership and the Purchasers are in the process of finalizing an asset
purchase agreement for the purchase and sale of all of the Partnership's assets,
subject to limited partner approval as discussed below. If the sale is
consummated, the General Partner will make one or more liquidating distributions
to the partners and, after providing for the payment of the Partnership's
obligations, cause the Partnership to dissolve and be liquidated. After
repayment of the Partnership's existing obligations, the Partnership presently
estimates that liquidating distributions to unitholders would total between $220
and $230 per unit, less applicable taxes, if any. The sale will require the
holders of at least a majority of the Partnership's limited partnership units to
consent to the sale, to certain amendments to the Partnership's partnership
agreement and to the liquidation.

          On September 30, 1997, the Partnership entered into a loan agreement
with EFC for a revolving loan facility of $2,528,900 (the "Facility") of which
$1,750,000 was advanced to the Partnership at closing. Such funds together with
available cash were used to repay the Partnership's previous note payable
balance of $1,077,100 and related interest expense, deferred management fees and
reimbursed expenses of $387,500 due the Corporate General Partner and deferred
programming fees of $408,000 owed to an affiliated partnership. The Partnership
prepaid $150,000 of its outstanding borrowings under the Facility on June 22,
1998. All outstanding borrowings under the Facility would be repaid in full with
the proceeds from the sale of the Partnership's assets as described above.

          The Partnership's Facility will mature on August 31, 2001, at which
time all funds previously advanced will be due in full. Borrowings bear interest
at the lender's base rate (8.5% at June 30, 1998) plus 0.625%, or at an offshore
rate plus 1.875%. The Partnership is permitted to prepay amounts outstanding
under the Facility at any time without penalty, and is able to reborrow
throughout the term of the Facility up to the maximum commitment then available
so long as no event of default exists. If the Partnership has excess cash flow
and its ratio of debt to cash flow exceeds 4.25 to 1, or it receives proceeds
from sales of its assets in excess of a specified amount, the Partnership is
required to make mandatory prepayments under the Facility. Such prepayments
permanently reduce the maximum commitment under the Facility.

          The Facility contains certain financial tests and other covenants
including, among others, restrictions on incurrence of indebtedness,
investments, sales of assets, acquisitions and other covenants, defaults and
conditions. The Partnership believes it was in compliance with the covenants at
June 30, 1998.

          The Facility does not restrict the payment of distributions to
partners unless an event of default exists thereunder or the ratio of debt to
cash flow is greater than 4 to 1. As previously disclosed, however, in response
to the FCC's amended rate regulation rules and the Partnership's capital
expenditure requirements, distributions to Unitholders were discontinued in July
1994. As stated at the time of the announcement of this decision, the
Partnership believes that it is critical to preserve its liquidity though the
retention of cash. As a result, and because of the pending system upgrade
requirements discussed above, the Partnership does


                                      -12-


<PAGE>   13
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

LIQUIDITY AND CAPITAL RESOURCES (CONTINUED)

not anticipate paying distributions at any time in the foreseeable future except
in connection with a liquidation of the Partnership as described above.

          The Corporate General Partner contributed $244,600 of its $632,100
receivable balance from the Partnership for past due management fees and
reimbursed expenses as an equity contribution to EFC. As a result, this balance
was not repaid on September 30, 1997 and remains an outstanding obligation of
the Partnership. Such receivable balance would be repaid from the proceeds of
the sale of the Partnership's assets as described above.

          Beginning in August 1997, the Partnership elected to self-insure its
cable distribution plant and subscriber connections against property damage as
well as possible business interruptions caused by such damage. The decision to
self-insure was made due to significant increases in the cost of insurance
coverage and decreases in the amount of insurance coverage available.

          While the Partnership has made the election to self-insure for these
risks based upon a comparison of historical damage sustained over the past five
years with the cost and amount of insurance currently available, there can be no
assurance that future self-insured losses will not exceed prior costs of
maintaining insurance for these risks. Approximately 90% of the Partnership's
subscribers are served by its system in Villa Rica, Georgia and neighboring
communities. Significant damage to the system due to seasonal weather conditions
or other events could have a material adverse effect on the Partnership's
liquidity and cash flows. The Partnership continues to purchase insurance
coverage in amounts its management views as appropriate for all other property,
liability, automobile, workers' compensation and other types of insurable risks.

          The "Year 2000" issue refers to certain contingencies that could
result from computer programs being written using two digits rather than four to
define the year. Many existing computer systems, including certain of the
Partnership's computer systems, process transactions based on two digits for the
year of the transaction (for example, "98" for 1998). These computer systems may
not operate effectively when the last two digits become "00," as will occur on
January 1, 2000.

          The Corporate General Partner has commenced an assessment of the
Partnership's Year 2000 business risks and its exposure to computer systems, to
operating equipment which is date sensitive and to the interface systems of its
vendors and service providers. Based on a preliminary study, the Corporate
General Partner has concluded that certain of the Partnership's information
systems were not Year 2000 compliant and has elected to replace such software
and hardware with Year 2000 compliant applications and equipment, although the
decision to replace major portions of such software and hardware had previously
been made without regard to the Year 2000 issue. The Corporate General Partner
expects to install substantially all of the new systems in 1998, with the
remaining systems to be installed in the first half of 1999. The total
anticipated cost, including replacement software and hardware, will be borne by
FHGLP.

          In addition to evaluating internal systems, the Partnership is
currently assessing its exposure to risks associated with its operating and
revenue generating equipment and has also initiated communications with
significant third party vendors and service suppliers to determine the extent to
which the Partnership's interface systems are vulnerable should those third
parties fail to solve their own Year 2000 problems on a


                                      -13-


<PAGE>   14
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

LIQUIDITY AND CAPITAL RESOURCES (CONTINUED)

timely basis. The Partnership currently expects that the cost to replace
non-compliant equipment will be determined during the third quarter of 1998.
Such costs will be borne by the Partnership. There can be no assurance that the
systems of other companies on which the Partnership's systems rely will be
timely converted and that the failure to do so would not have an adverse impact
on the Partnership's business. The Partnership continues to closely monitor
developments with its vendors and service suppliers.

          SIX MONTHS ENDED JUNE 30, 1998 AND 1997

          Cash provided by operating activities decreased by $203,100 in the six
months ended June 30, 1998 from the corresponding period in 1997. Changes in
receivables and prepaid expenses provided $218,900 less cash in the first six
months of 1998 primarily due to the collection of an insurance claim in the
first three months of 1997. The Partnership used $3,000 less cash for accounts
payable in the first half of 1998 due to differences in the timing of payments.

          The Partnership used $27,600 more cash in investing activities during
the six months ended June 30, 1998 than in the comparable six months of 1997 due
to increases of $21,100 in expenditures for tangible assets and $7,400 in
spending for intangible assets. Financing activities used $541,100 less cash in
the first six months of 1998 than in the comparable 1997 period. The Partnership
used $481,100 more cash in the first half of 1997 than in the equivalent period
of 1998 to pay past due balances for management fees and reimbursed expenses
owed to the Corporate General Partner and programming expense owed to
Cablevision. Additionally, the Partnership used $61,300 less cash for the
repayment of debt in the 1998 period, partially offset by an increase of $1,300
in expenditures for deferred loan costs related to its Facility with EFC.

INFLATION

          Certain of the Partnership's expenses, such as those for equipment
repair and replacement, billing and marketing generally increase with inflation.
However, the Partnership does not believe that its financial results have been,
or will be, adversely affected by inflation in a material way, provided that it
is able to increase its service rates periodically, of which there can be no
assurance.


                                      -14-


<PAGE>   15
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

PART II.                OTHER INFORMATION


ITEMS 1-5.              Not applicable.

ITEM 6.                 Exhibits and Reports on Form 8-K

                        (a)        Exhibit 10.25 - Franchise Ordinance thereto
                                   granting a non-exclusive community antenna
                                   television franchise for the City of Bowdon,
                                   Georgia and a resolution amending the 
                                   franchise agreement.

                        (b)        No reports on Form 8-K were filed during the
                                   quarter for which this report is filed.


<PAGE>   16
                                   SIGNATURES


Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.





                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.

                          a GEORGIA LIMITED PARTNERSHIP
                          -----------------------------
                                  (Registrant)


                                       
                                      By: ENSTAR COMMUNICATIONS CORPORATION
                                          General Partner






Date:  August 13, 1998                By:   /s/ Michael K. Menerey
                                           -----------------------------
                                           Michael K. Menerey,
                                           Executive Vice President,
                                           Chief Financial Officer and 
                                           Secretary


<PAGE>   17
                    ENSTAR INCOME/GROWTH PROGRAM SIX-B, L.P.


                                  EXHIBIT INDEX


Exhibit
Number                                         Description


10.25     Franchise Ordinance thereto granting a non-exclusive community antenna
          television franchise for the City of Bowdon, Georgia and a resolution 
          amending the franchise agreement.


                                       E-1