Well, I don't reccomend it, but I used a calculator because I'm too lazy.
\(729y^{12}+2916y^{11}-2430y^{10}-19980y^9+135y^8+59976y^7+6364y^6-99960y^5+375y^4+92500y^3-18750y^2-37500y+15625\)
As you can see, the coefficient for y^4 is 375.
Thanks! :)