Answer
$4x$
Work Step by Step
The $GCF$ of $
12
$ and $
8
$ is $
4
.$
The $GCF$ of $
x^2
$ and $
x^1
$ is $
x^1
.$
Hence, the $GCF$ of the given expressions, $
12x^2 \text{ and } 8x
,$ is
\begin{array}{l}\require{cancel}
4x^1
\\\\=
4x
.\end{array}