not sure if my logic is right, but this is how i arrived at C as my first guess
the O-C=O group is deactivating, so it stabilizes the molecule making it a weak base. II happens to have 2 carbonyl groups, so it is the weakest base (the most stable) therefore it has the strongest conjugate acid. IV has less of a stabilizing affect, but it has more of a stabilizing affect than III (which also has a carbonyl group)
So the H in the middle of two carbonyl is very acidic bc it has two electron withdrawing groups on each side. III is the next most acidic bc of the carbonyl. Then IV bc esters are not very reactive but their Hs are def more acidic than an alkane...
Hope this helps
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