Answer
$2xy(2xy^2+3)$
Work Step by Step
Factoring the $GCF=
2xy
,$ the given expression, $
4x^2y^3+6xy
,$ is equivalent to
\begin{array}{l}\require{cancel}
2xy
\left(
\dfrac{4x^2y^3}{2xy}+\dfrac{6xy}{2xy}
\right)
\\\\=
2xy(2xy^2+3)
.\end{array}