Answer
$-20a^2+29ab+48b^2$
Work Step by Step
Using $a(b+c)=ab+ac$ or the Distributive Property, the given expression, $
-8a^2+5ab-12b^2-6(2a^2-4ab-10b^2)
$, is equivalent to
\begin{array}{l}\require{cancel}
-8a^2+5ab-12b^2-6(2a^2)-6(-4ab)-6(-10b^2)
\\\\=
-8a^2+5ab-12b^2-12a^2+24ab+60b^2
.\end{array}
By combining like terms, then this simplifies to
\begin{array}{l}\require{cancel}
(-8a^2-12a^2)+(5ab+24ab)+(-12b^2+60b^2)
\\\\=
-20a^2+29ab+48b^2
.\end{array}
