Answer
$3xy^{2}(3x^{2}+4xy^{2}-y^{3})$
Work Step by Step
$12x^{2}y^{4}-3xy^{5}+9x^{3}y^{2}$
Take out common factor $3xy^{2}$:
$12x^{2}y^{4}-3xy^{5}+9x^{3}y^{2}=3xy^{2}(4xy^{2}-y^{3}+3x^{2})=...$
Rearrange:
$...=3xy^{2}(3x^{2}+4xy^{2}-y^{3})$