Answer
$3x^2y$
Work Step by Step
\begin{align*}
\text{The $GCF$ of $
6,
9,
\text{ and }
12
\text{ is }
3
$}
.\\\\
\text{The $GCF$ of $
x^3,
x^2,
\text{ and }
x^2
\text{ is }
x^2
$}
.\\\\
\text{The $GCF$ of $
y,
y^2,
\text{ and }
y
\text{ is }
y
$}
.\end{align*}
Hence, the $GCF$ of the given expressions is $3x^2y$.