Answer
$\begin{bmatrix}
{-2}&{4}&{2}&{8}\\
{2}&{1}&{4}&{6}\end{bmatrix}$
Work Step by Step
Since $A$ is a $2 \times 2 $ matrix and $B$ is a $2 \times 4$ matrix, the product $AB$ is defined and equals a $2 \times 4$ matrix.
Thus,
$AB \\=\begin{bmatrix}
(2)(2)+(-2)(3) & (2)(1)+(-2)(-1) & (2)(4)+(-2)(3) & (2)(6)+(-2)(2)\\
(1)(2)+(0)(3) & (1)(1)+(0)(-1) & (1)(4)+(0)(3) & (1)(6)+(0)(2)
\end{bmatrix} \\=\begin{bmatrix}
{-2}&{4}&{2}&{8}\\
{2}&{1}&{4}&{6}\end{bmatrix}$