Answer
$3xy(2x^2y+3)$
Work Step by Step
Factoring the $GCF=
3xy
,$ the given expression, $
6x^3y^2+9xy
,$ is equivalent to
\begin{array}{l}\require{cancel}
3xy
\left(
\dfrac{6x^3y^2}{3xy}+\dfrac{9xy}{3xy}
\right)
\\\\=
3xy(2x^2y+3)
.\end{array}