Answer
$\begin{bmatrix}
-26&-22\\
-54&-13
\end{bmatrix}$
Work Step by Step
If the dimensions of matrix A are $a\times b$ and the dimensions of matrix C are $c\times d$, then AC is defined if $b=c$, and then AC has dimensions $a\times d.$
Hence here:
$AC=\begin{bmatrix}
1\cdot-6+(-2)\cdot10&1\cdot8+(-2)\cdot15\\
4\cdot-6+(-3)\cdot10&4\cdot8+(-3)\cdot15
\end{bmatrix}
=\begin{bmatrix}
-26&-22\\
-54&-13
\end{bmatrix}$
