Answer
$\left[\begin{array}{rrrr}
{-2}&{4}&{2}&{8}\\
{2}&{1}&{4}&{6}\end{array}\right]$
Work Step by Step
Let $A$ denote an $m$ by $\fbox{$r$}$ matrix and let $B$ denote an $\fbox{$r$}$ by $n$ matrix.
The product $AB$ is defined as the $m$ by $n$ matrix whose entry in row $i,$ column $j$
is the product of the $i$ th row of $A$ and the $j$ th column of $B$ .
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$A$ is a $2$ by $\fbox{$2$}$ matrix and B is a $\fbox{$2$}$ by $4$ matrix.
The product $AB$ is defined, and is a $2$ by $4$ matrix.
$AB=\\\left[\begin{array}{llll}
2(2)+(-2)(3) & 2(1)+(-2)(-1) & 2(4)+(-2)(3) & 2(6)+(-2)(2)\\
1(2)+(0)(3) & 1(1)+(0)(-1) & 1(4)+(0)(3) & 1(6)+(0)(2)
\end{array}\right]$
$=\left[\begin{array}{rrrr}
{-2}&{4}&{2}&{8}\\
{2}&{1}&{4}&{6}\end{array}\right]$
