This is a numbered ordering game - I've attached my diagram.
Let's take a look at # 2 to see how we'd use the diagram. If S and G are on odd numbered hangers, what do we know? Well, for starters we know that there are only 3 odd numbered hangers: 1, 3, and 5. This probably gives us a few too many possibilities to diagram them all out but one thing is important to note - this doesn't necessarily mean that S is on the third hanger. Let's take a look at our answer choices to see which could be true.
(A) can't be true ever - we've already inferred that in the original diagram.
(B) works - consider RWSLGP. This must be our answer. On the LSAT, I'd pick this and move on, but let's check out some of the other possibilities.
(C) doesn't work because the odd numbers get filled up. In particular, if P is on 4, then S can't be on 3 (since we have SL) so W must be on 3. We can put S on 5 (G can't go there since it has to be before P) and L on 6, which means R must go on 1 - and oops! We've run out of odd numbered hangers without assigning G. It's not possible to do otherwise.
(D) doesn't work because it means that S is on 4, an even number.
(E) If W is on 6, then S is on 3, L is on 4, and R is on 1. That leaves only 5 as an odd numbered hanger, but then we'll violate the constraint requiring that G go before P.
I hope this helps. Any questions or comments?