#### Answer

$(2-x)(2-y)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Group the terms of the given expression, $
4+xy-2y-2x
,$ 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 fourth terms and the second and third terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(4-2x)+(xy-2y)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2(2-x)+y(x-2)
\\\\=
2(2-x)-y(2-x)
.\end{array}
Factoring the $GCF=
(2-x)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(2-x)(2-y)
.\end{array}