Question

My cousins _____ letters.

A. Write
B. Sit
C. Writes

Answer 1

A, say it out loud, it's what makes the most sense.
Sit is automatically eliminated.
Writes would be, my cousin writes me letters. Its a current action.
Since you're saying more than one cousin, it is, My cousins write letters.

Answer 2

A. write is the correct answer