Hi JoelKananelo!
Remember Pascal's triangle (These numbers are the coefficients!)
1 (a+b)^0
1 1 (a+b)^1
1 2 1 (a+b)^2
1 3 3 1 (a+b)^3
1 4 6 4 1 (a+b)^4
1 5 10 10 5 1 (a+b)^5
1 6 15 20 15 6 1 (a+b)^6
We are interested in the last row:
Let \(a=3x \\ b=-4y\)
Hence,
\((a+b)^6=a^6+6a^5b+15a^4b^2+20a^3b^3+15a^2b^4+6ab^5+b^6\)
So,
\((3x-4y)^6=(3x)^6+6(3x)^5(-4y)+15(3x)^4(-4y)^2+20(3x)^3(-4y)^3+15(3x)^2(-4y)^4+6(3x)(-4y)^5+(-4y)^6\)
Simplify this and you should get your answer!
I hope this helps :)