Answer
$(m-3q)(2x+2y)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
2mx-6qx+2my-6qy
,$ such that the factored form of the groupings will result to a factor common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression.
$\bf{\text{Solution Details:}}$
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(2mx-6qx)+(2my-6qy)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2x(m-3q)+2y(m-3q)
.\end{array}
Factoring the $GCF=
(m-3q)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(m-3q)(2x+2y)
.\end{array}