Determining and Differentiating specific ATPases
First of all, I think you need to research the subunit structures of the various ATPase classes in the list because I am pretty sure that several of them are not as complex as this.

Although this superficially looks like the F-ATPase responsible for synthesising ATP by using the proton gradient generated by the electron chain, there is a clue in that diagram that this may actually be a V-ATPase. The V-ATPases use ATP hydrolysis to move protons from the cytoplasm into the lumen of acidic organelles like lysosomes. The diagram in the question depicts a process like that (ATP is being hydrolysed). Now, you can drive the F ATPase in reverse to achieve this situation, so that isn't definitive. 

The labelling of the two compartments is also consistent with the idea that it is a V-ATPase since 'lumen' isn't a word that is usually used in the context of the mitochondrion (it would normally be 'matrix').

So I would suggest that you find out if the subunit labelling is like that used in F-ATPase or V-ATPase (or both). A Google image search will help you to find cartoons of ATPases.

My guess, before doing the suggested research, is that this is a V-ATPAse.