Question: What is this census-designated place (CDP) in New York with around a population of 4,000 as of 2010 and belongs to Mattituck-Cutchogue Union Free School District?

Context paragraphs:
Mattituck, New York: Mattituck is a hamlet and census-designated place (CDP) in Suffolk County, New York, United States.  The population was 4,219 at the 2010 census.

Eatons Neck, New York: Eatons Neck is a hamlet and census-designated place (CDP) in the Town of Huntington, Suffolk County, New York, United States.  The population was 1,406 at the 2010 census.  Students attend the Northport-East Northport Union Free School District.  There is a United States Coast Guard station on the northern tip of Eatons Neck.

Southold Union Free School District: Southold Union Free School District is a public school district located on the North Fork of Long Island, in Suffolk County, New York, United States.  It serves the central portion of the Town of Southold, including the majority of the census-designated place(CDP) of Southold, as well as the eastern portion of the CDP of Peconic.  To the east, the district is bordered by the Greenport Union Free School District; and on the west, the Mattituck-Cutchogue Union Free School District.

Hauppauge Union Free School District: Hauppauge Union Free School District is a school district based in Hauppauge, New York.  It is near the Commack School District and Half Hollow Hills Central School District, as well as the Syosset Central School District and Jericho Union Free School District in Nassau County

Garden City Union Free School District: Garden City Union Free School District is headquartered at 56 Cathedral Avenue in Garden City, NY 11530 (phone 516-478-1000).  The Garden City Union Free School District is rated 35th in New York and 74th overall in the country.

Bridgehampton Union Free School District: Bridgehampton Union Free School District is a public school district located in the Town of Southampton on Long Island, in Suffolk County, New York, United States.  It is roughly co-extensive with the hamlet (and census-designated place) of Bridgehampton.

Jericho, New York: Jericho is a hamlet and census-designated place (CDP) in Nassau County, New York on the North Shore of Long Island.  As of the United States 2010 Census, the CDP population was 13,567.  The area is served by the Jericho Union Free School District and the Syosset Central School District, the boundaries of which differ somewhat from those of the hamlet.  The boundaries of the Jericho Post Office vary from both the hamlet and the school district boundaries, notably the inclusion of a portion of Jericho in the Westbury zip code, and the inclusion of a portion of Syosset in the Jericho zip code.  Also, Jericho is located approximately 29 miles (47 km) east of Midtown Manhattan.  Direct service is available by driving west on the Long Island Expressway or one can take the Long Island Rail Road from nearby Hicksville or Syosset train station.

Greenport Union Free School District: Greenport Union Free School District is a public school district located on the North Fork of Long Island, in the Town of Southold, Suffolk County, New York, United States.  It includes the village of Greenport, as well as the census-designated place(CDP) of Greenport West.  To the west, the district is bordered by the Southold Union Free School District; and on the east, the Oysterponds Union Free School District.

Oysterponds Union Free School District: Oysterponds Union Free School District is a public school district located in the Town of Southold Suffolk County, New York, United States.  It is the easternmost school district on the North Fork of Long Island.  The district includes the census-designated places(CDPs) of East Marion and Orient.  To the west, the district is bordered by the Greenport Union Free School District.

Mattituck-Cutchogue Union Free School District: Mattituck-Cutchogue Union Free School District is a public school district located on the North Fork of Long Island, in Suffolk County, New York, United States.  It primarily serves the western part of the Town of Southold, as well as a small portion of the Town of Riverhead, and includes the census-designated places of Mattituck, Cutchogue and Laurel, and portions of Jamesport and Peconic.  To the east, the district is bordered by the Southold Union Free School District; and on the west, the Riverhead Central School District.

Supporting paragraphs: Mattituck-Cutchogue Union Free School District Mattituck, New York
Answer: Mattituck