how do u prove or disprove the distance to a galaxy of 15 million light years away?

Answer 1

You can't prove it, but there is a lot of evidence that the universe is expanding. There is a red-shift in the radiation emitted from objects traveling away from us, and the further away an object is, the faster it will be moving away from us.

So, we simply look for the degree of red-shift, and it tells us approximately how far away the galaxy is.

Answer 2

Look up Cepheid variable stars and redshift / Doppler shift.