Answer
$(x+2+y)(x+2-y)$
Work Step by Step
The first $3$ terms of the given expression, $
x^2+4x+4-y^2
,$ is a perfect square trinomial. Hence, the factored form is
\begin{array}{l}\require{cancel}
(x+2)^2-y^2
.\end{array}
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the sum and difference of like terms, then the completely factored form of the expression, $
(x+2)^2-y^2
,$ is
\begin{array}{l}\require{cancel}
[(x+2)+y][(x+2)-y]
\\\\=
(x+2+y)(x+2-y)
.\end{array}