which counties does it pass through?
Schoharie County.
New York State Route 146
 The highway spends only in Schoharie County before passing into neighboring Albany County. Along this stretch, NY 146 has an intersection with County Route 26 (CR 26, named Larry Hill Road) just over from NY 443. 
which places are connected by new york state route 146? Gallupville, Mechanicville and Schenectady.
wiki:23139964
New York State Route 146 [SEP] Schoharie and Albany counties
NY 146 heads east from Maple Avenue, following Main Street eastward out of the village. After leaving Altamont, NY 146 continues for about through a lightly populated portion of Guilderland before intersecting with the southern terminus of NY 158. The route progresses onward, intersecting CRs 201 and 202 and passing over the CSX Transportation-owned Selkirk Subdivision railroad line and Normans Kill before meeting US 20 at Hartmans Corners. NY 146 joins US 20 for about northwestward to McCormack Corners, where NY 146 leaves US 20 and heads northward toward Schenectady County. The route passes over the New York State Thruway (Interstate 90 or I-90) just south of the county line.