What could a hand x-ray show?

Many things: Among others, an xray of a hand could show bone deformities, fractures, arthritis, gout, osteoporosis, necrosis, foreign body and even cancer.

And some other things: I agree with dr. Suchecki, and would add that there are lots of things that an x-ray -won't- show, like carpal tunnel syndrome, trigger fingers, cysts, and tendon injuries. An x-ray may still be helpful, but could be "normal" in those conditions.