How do I solve this problem?

(4x+2y)(x-3y)
This is the answer I've got but I don't think it's correct:
4x*x= 4x^2
2y*-3y=-6y^2
4x^2 - 6y^2

Multiply each term in one polynomial by each term in the other polynomial.

( 4 x + 2 y ) ( x - 3 y ) =

x * 4 x + x * 2 y - 3 y * 4 x - 3 y * 2 y =

4 x ^ 2 + 2 x y - 12 x y - 6 y ^ 2 =

4 x ^ 2 - 10 x y - 6 y ^ 2