Answer
$6xy\sqrt{2y}-8xy\sqrt{2y}$
Work Step by Step
Using the properties of radicals, the given expression, $
3\sqrt{8x^2y^3}-2x\sqrt{32y^3}
,$ simplifies to
\begin{array}{l}\require{cancel}
3\sqrt{4x^2y^2\cdot2y}-2x\sqrt{16y^2\cdot2y}
\\\\=
3\sqrt{(2xy)^2\cdot2y}-2x\sqrt{(4y)^2\cdot2y}
\\\\=
3\cdot2xy\sqrt{2y}-2x\cdot4y\sqrt{2y}
\\\\=
6xy\sqrt{2y}-8xy\sqrt{2y}
.\end{array}