Answer
$\dfrac{x+2y}{4-x}$
Work Step by Step
The given expression, $
\dfrac{xz-xw+2yz-2yw}{z^2-w^2}\cdot\dfrac{4z+4w+xz+wx}{16-x^2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(xz-xw)+(2yz-2yw)}{z^2-w^2}\cdot\dfrac{(4z+4w)+(xz+wx)}{16-x^2}
\\\\=
\dfrac{x(z-w)+2y(z-w)}{(z-w)(z+w)}\cdot\dfrac{4(z+w)+x(z+w)}{(4+x)(4-x)}
\\\\=
\dfrac{(z-w)(x+2y)}{(z-w)(z+w)}\cdot\dfrac{(z+w)(4+x)}{(4+x)(4-x)}
\\\\=
\dfrac{(\cancel{z-w})(x+2y)}{(\cancel{z-w})(\cancel{z+w})}\cdot\dfrac{(\cancel{z+w})(\cancel{4+x})}{(\cancel{4+x})(4-x)}
\\\\=
\dfrac{x+2y}{4-x}
.\end{array}
