#### Answer

$2xy(x+3)(x-2)$

#### Work Step by Step

Factoring the $GCF=2xy$, then the given expression, $
2x^3y+2x^2y-12xy
$, is equivalent to
\begin{array}{l}
2xy(x^2+x-6)
.\end{array}
The two numbers whose product is $ac=
1(-6)=-6
$ and whose sum is $b=
1
$ are $\{
3,-2
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
2xy(x^2+x-6)
$, is
\begin{array}{l}\require{cancel}
2xy(x^2+3x-2x-6)
\\\\=
2xy[(x^2+3x)-(2x+6)]
\\\\=
2xy[x(x+3)-2(x+3)]
\\\\=
2xy[(x+3)(x-2)]
\\\\=
2xy(x+3)(x-2)
.\end{array}