Answer
$-3(y+2)^2$
Work Step by Step
Factoring the negative $GCF=-3,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
-3y^2-12y-12
\\\\=
-3(y^2+4y+4)
.\end{array}
Using the factoring of trinomials in the form $x^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
-3(y^2+4y+4)
\end{array} has $c=
4
$ and $b=
4
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
2,2
\right\}.$ Using these two numbers, the $\text{
expression
}$ above is equivalent to
\begin{array}{l}\require{cancel}
-3(y+2)(y+2)
\\\\=
-3(y+2)^2
.\end{array}