Answer
$-\dfrac{3}{2}$
Work Step by Step
Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, the given expression, $
\dfrac{4-x}{5}\cdot \dfrac{15}{2x-8}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{-(x-4)}{5}\cdot \dfrac{5\cdot3}{2(x-4)}
\\\\=
\dfrac{-(\cancel{x-4})}{\cancel{5}}\cdot \dfrac{\cancel{5}\cdot3}{2(\cancel{x-4})}
\\\\=
\dfrac{-3}{2}
\\\\=
-\dfrac{3}{2}
.\end{array}