That looks like a 1644: year maybe 78??? It looks to be in good condition!
Briarpatch
It's not a 1644. It looks like a 1643 to me.
My understanding of the Tucker nomenclature of that era is as follows:
First two digits refer to the track length. 13xx have short tracks (four idler wheels). 15xx have mid length tracks (five idler wheels). 16xx have long tracks (six idler wheels) 17xx are heavy duty versions of the 1600 series.
Third digit (4) refers to the fact that it is a four track machine.
Fourth digit refers to the number of doors.
This is a three door "sedan" model and has a door at the back of the machine. The two front seats face forward and the rear seating is what I'll call "troop seats"; bench style seats that face each other.