Answer
$28x^{4}y^{2}+12x^{3}y^{4}-36xy^{5}$
Work Step by Step
$4xy^{2}(7x^{3}+3x^{2}y^{2}-9y^{3})=(4xy^{2})(7x^{3})+(4xy^{2})(3x^{2}y^{2})+(4xy^{2})(-9y^{3})=28x^{1+3}y^{2}+12x^{1+2}y^{2+2}+(-36xy^{2+3})=28x^{4}y^{2}+12x^{3}y^{4}+(-36xy^{5})=28x^{4}y^{2}+12x^{3}y^{4}-36xy^{5}$