how to solve this puzzle?


Well if you don't have a limit on your moves the answer is absurdly easy. If you meant a mate in two (which you didn't specify) it's a bit trickier to see Qe3 since it's so counterintuitive, although logical.

I didn't have a problem making out the pieces, but yeah it doesn't make sense to have them such a small size. Why not edit your post and put a bigger board in + add "White to mate in 2"?