For this problem, can't you remove a hydrogen from either alpha carbon of the carbonyls? You would get two different products though (b and e) so how do you know which one is right?

Yes you can do it the other way around. But the answer b will be the major product because of the steric hinderance. However, you should know the structure of choice e is completely wrong. Compare the substituents on choice b with e, you will see why. :)