The answer must be Option B.

We can rephrase the target question as follows:

is bx2- by2>0

is b(x+y)(x-y)>0?

Now statement I says b>0, no information about x and y, thus data is clearly insufficient. No need to think twice on this. Options reduced to BCE

Statement II says b3(|x|-|y|)>0. Now, there are two ways to expand this:

Either
b3>0 and |x|-|y|>0 -CASE I
OR
b3<0 and |x|-|y|<0-CASE II

Now some logic will come in play.

CASE I

b3>0 means b >0 and |x|-|y|>0 means x2-y2>0 (squaring both the sides and taking terms on one side). Now plug this in the original question stem, the data is sufficient. (+VE X +VE GIVES +VE VALUE)

Similarly,
CASE II

b3<0 means b <0 and |x|-|y|<0 means x2-y2<0 (squaring both the sides and taking terms on one side). Now plug this in the original question stem, the data is sufficient. (-VE X -VE GIVES -VE VALUE)

In either case, the answer to the original question stem is DEFINITE YES.

Thus, statement II alone is sufficient.

Thank You
Vighnesh