Answer
$-(xy+2)(xy+6)$
Work Step by Step
The given expression, $
-12-x^2y^2-8xy
,$ can be re-written as
\begin{array}{l}
-x^2y^2-8xy-12
\\\\=
-(x^2y^2+8xy+12)
.\end{array}
The two numbers whose product is $ac=
1(12)=12
$ and whose sum is $b=
8
$ are $\{
2,6
\}$. Using these two numbers to decompose the middle term of the expression, $
-(x^2y^2+8xy+12)
,$ then the factored form is
\begin{array}{l}
-(x^2y^2+2xy+6xy+12)
\\\\=
-[(x^2y^2+2xy)+(6xy+12)]
\\\\=
-[xy(xy+2)+6(xy+2)]
\\\\=
-[(xy+2)(xy+6)]
\\\\=
-(xy+2)(xy+6)
.\end{array}
