Question: New York State Route 406 (NY 406) is a state highway in Schenectady County, New York, the western terminus of the route is at an intersection with U.S. Route 20 (US 20) in which town in Schenectady County, New York?
Context: New York State Route 39 (NY 39) is an east–west state highway in the western portion of New York in the United States.  It begins and ends at intersections with U.S. Route 20 (US 20) 98.89 mi apart.  The western terminus of NY 39 is east of Fredonia in the Chautauqua County town of Sheridan, while the eastern terminus is in the Livingston County village of Avon.  At its east end, NY 39 also ends at NY 5, which is concurrent to US 20 at this point.  NY 39 serves several villages, including Gowanda and Geneseo, and intersects a handful of major north–south highways, such as US 219 in Springville and NY 19 near Pike.  Most of the route is a two-lane highway that passes through rural, undeveloped areas. New York State Route 406 (NY 406) is a state highway in Schenectady County, New York, in the United States.  The western terminus of the route is at an intersection with U.S. Route 20 (US 20) in the town of Princetown.  Its eastern terminus is at a junction with NY 158 in the town of Rotterdam.  NY 406 is a two-lane highway and known as Giffords Church Road along its entire length.  It was assigned to its current alignment in the mid-1930s. Princetown is a town in Schenectady County, New York, United States.  The population was 2,115 at the 2010 census.  It is in the central part of the county, west of the town of Rotterdam. New York State Route 20SY (NY 20SY) was a state highway in the vicinity of Syracuse, New York, in the United States.  It connected U.S. Route 20 (US 20) to downtown Syracuse via Skaneateles, Camillus, Manlius, and Cazenovia in Onondaga County and Madison County.  The highway began at an intersection with US 20 and NY 321 in the village of Skaneateles and ended at a junction with US 20, NY 20N, and NY 92 near the village of Cazenovia.  Most of NY 20SY overlapped another route; however, two sections of NY 20SY—one in the town of Camillus and another near the village of Fayetteville—were not concurrent with another highway. New York State Route 318 (NY 318) is an east–west state highway in the Finger Lakes region of New York in the United States.  The western terminus of the route is at an intersection with NY 14 at New York State Thruway (Interstate 90 or I-90) exit 42 in the town of Phelps.  The eastern terminus is at an intersection with U.S. Route 20 (US 20) and NY 5 northeast of the hamlet of Seneca Falls.  All but 0.70 mi of the 10.90 mi route is located in Seneca County. New York State Route 162 (NY 162) is a state highway in eastern New York in the United States.  It runs from an intersection with U.S. Route 20 (US 20) in the Schoharie County town of Esperance to an interchange with NY 5S in the Montgomery County town of Root, west of the village of Canajoharie.  The southernmost 0.75 mi of the route are concurrent with NY 30A, which continues south of NY 162's intersection with US 20.  NY 162 is a two-lane highway for all of its length, although its final 1.25 mi has a climbing lane southbound as it leaves the Mohawk Valley over the Sprakers Gorge.  The route was assigned as part of the 1930 renumbering of state highways in New York and realigned slightly in the late 1960s to bypass an accident-prone stretch near its northern terminus. New York State Route 166 (NY 166) is a north–south state highway in Otsego County, New York, in the United States.  It extends for 20.96 mi from NY 28 in the village of Milford to U.S. Route 20 (US 20) north of the village of Cherry Valley.  Much of NY 166's southern portion is near Cooperstown, and various county routes serve as connectors between NY 166 and Cooperstown.  In Cherry Valley, NY 166 intersects the former western terminus of the First Great Western Turnpike.  After passing under US 20, the road continues as County Route 32 north to Sprout Brook in Montgomery County, where it meets NY 163.  NY 166 is a two-lane highway its entire length. U.S. Route 20A (US 20A) is an east–west alternate route of US 20 that extends for 83.59 mi across the western portion of New York in the United States.  It leaves US 20 in Hamburg, a suburb of Buffalo, and rejoins it in East Bloomfield about five miles (8 km) west of Canandaigua, the county seat of Ontario County.  The western terminus is situated just northeast of the intersection of US 20 and US 62 and west of Ralph Wilson Stadium.  At its east end, US 20A also meets New York State Route 5 (NY 5) and NY 64.  Most of the route is known as Big Tree Road; outside Ralph Wilson Stadium, the highway is known as the Timothy J. Russert Highway in memory of Buffalo native Tim Russert. New York State Route 151 (NY 151) is an 8.23 mi state highway located in Rensselaer County, New York, in the United States.  Its western terminus is at an interchange with U.S. Route 9 (US 9) and US 20 in Rensselaer, and its eastern terminus is at a junction with NY 150 in Shivers Corners, a hamlet in the town of Schodack.  It also has an intersection with US 4 in East Greenbush.  NY 151 was assigned to most of its current alignment as part of the 1930 renumbering of state highways in New York.  In Rensselaer, NY 151 has been altered several times, with the most recent change coming in the late 1990s.  The current western terminus of NY 151 was once the western terminus of NY 43. New York State Route 20N (NY 20N) was a state highway in central New York in the United States.  It was an alternate route of U.S. Route 20 (US 20) that stretched for 30.5 mi between Marcellus and Cazenovia.  The road began at its parent route, US 20, and NY 174 in Marcellus and ended at US 20, NY 20SY, and NY 92 in Cazenovia.  All of NY 20N was concurrent with at least one other route, namely NY 174 in Marcellus, NY 175 from Marcellus to Onondaga Hill, NY 173 from Onondaga Hill to Manlius, and NY 92 and NY 20SY between Manlius and Cazenovia.  NY 20N was assigned in May 1937 and removed in 1961 along with NY 20SY.
Answer: Princetown