Probably the quickest way is to just multiply the original expression modulo 11 and check each of the answers.
3x + 7y = 0 (mod 11),
then by multiplying by 4 we find that
x + 6y = 0 (mod 11),
so adding both together shows that
4x + 2y = 0 (mod 11).
This is the same as
4x - 9y (mod 11),
so the answer is D.