HI ziyuenlau,

This question can be solved by TESTing VALUES.

We're told that X > Y. We're asked if |X| > |Y|. This is a YES/NO question.

1) X > 0

IF....
X = 1, Y = 0, then the answer to the question is YES
X = 1, Y = -2, then the answer to the question is NO
Fact 1 is INSUFFICIENT

2) Y > 0

Here, since Y is POSITIVE, X must ALSO be positive. Since we already know that X > Y, dealing with two POSITIVE values means that |X| will ALWAYS be greater than |Y|. Thus the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

It can be helpful when approaching a DS yes/no question to ask yourself: when would we get a NO answer?

In this case, when would the absolute value of x *NOT* be greater than y, if x itself is greater than y?
The only time that would be the case is if y is a negative number further away from 0 than x (whether x is positive or negative). If they were both positive, x would have to be further from 0 than y is, i f x > y. So we could rephrase the question as:
Is y positive?

If you frame the question that way before looking at the statements, it's clear that statement 1 is insufficient, but statement 2 is sufficient.