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