Answer
$$ g^2 -3g - h^2 + 9h -18 .$$
Work Step by Step
We multiply each term of the first polynomial by each term of the second polynomial. Then we add the products, as follows
$$ (g + h -6)(g - h + 3)= g (g - h + 3)+ h(g - h + 3) -6(g - h + 3)\\ =g^2 -g h + 3g+ hg - h^2 + 3h -6g +6 h -18\\ = g^2 -3g - h^2 + 9h -18 .$$
