Q:

Holt-Winters exponential smoothing formula

I am trying to implement Holt-Winters exponential smoothing in Java program (I understand that R and Python have implementations of these algorithms, but I can't use those due to other reasons, so they are ruled out). 
I have been going through Rob J. Hyndman's book and formula.  I am trying to execute the following formula on my sample data manually, but I'm having a hard time understanding some of the notations.  If I can run it manually, I can start implementing in code:
Let us say we have 12 data points (Monthly data for a year): 8,9,10,7,9,10,9,8,9,8
The last 8 in this data represents current month data, and I want to forecast the next 3 months' values (which will be something like 9,9,8, I assume).  How can I use the formula listed in the above link to get these values is the part with which I am struggling. 
Specially I am not clear with two things:

What does $\hat{y}_{t+h|t}$ represent?  Is it next month's value (or) next value from the starting point? 
How can I calculate the $s_{t-m+h_m^+}$ value? 

Any pointers to get started on manual calculation would be appreciated.  Thanks for your time and help. 

A:

I made code for python that can be found here if you want to check it out.  It is fairly easy to understand. 
y(t+h) is the last point of data you have with the addition of h steps ahead.  For example if you forecast 3 months ahead it would be at point t +3
What I used to make my code was the NIST site.  
For your second question I think you are calculating the seasonal data.  I am not sure what you mean by s((t-m)+hm+). 
If you do not want to implement it yourself here is a java implementation I found

