[High school Physics] help understanding a formula - why masses cancel out in a problem?

http://i.imgur.com/SCmyY9X.jpg

So the question is at the top obviously. Under that is the formula I used. Actually, my teacher did this and I need help understanding why the masses/mass cancels out when I actually perform the calculation.

Is it because the masses are the same on both sides of the = sign? I just don't understand why the masses cancel out, even if they're the same - they impact the formulas.

To add, why don't the 2 gravities in the mgh's cancel out?