As it is written in your post, the correct answer is A

If x and y are POSITIVE integers, is (4^x)(1/3)^y < 1?

1) y = 2x
2) y = 4

Target question: Is (4^x)(1/3)^y < 1?

Statement 1: y = 2x
IMPORTANT CONCEPT #1: (1/3)^2x = [(1/3)^2]^x = (1/9)^x
IMPORTANT CONCEPT #2: (a^n)(b^n) = (ab)^n

Take the target question and replace y with 2x to get: Is (4^x)(1/3)^2x < 1?
Apply concept #1 to get: Is (4^x)(1/9)^x < 1?
Apply concept #2 to get: Is (4/9)^x < 1?
If x is a POSITIVE integer, it must be the case that (4/9)^x < 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y = 4
There are several possible conflicting cases. Here are two:
Case a: x = 1 and y = 4, in which case (4^x)(1/3)^y < 1
Case b: x = 10 and y = 4, in which case (4^x)(1/3)^y > 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent