Answer
$\left[\begin{array}{ccc}
{14}&{7}&{-2}\\
{20}&{12}&{-4}\\
{-14}&{7}&{-6}\end{array}\right]$
Work Step by Step
Since, matrix $A$ and $B$ are both $ 2 \times 3$ matrices and have the same dimensions and $C$ matrix $3 \times 2$ , we know that $CB$, is defined and is a 3 by 3 matrix.
$CB=\left[\begin{array}{ll}
4 & 1\\
6 & 2\\
-2 & 3
\end{array}\right]\left[\begin{array}{lll}
4 & 1 & 0\\
-2 & 3 & -2
\end{array}\right] \\=\left[\begin{array}{ccc}
{(4)(4)+(1)(-2)}&{(4)(1)+(1)(3)}&{(4)(0)+(1)(-2)}\\
{(6)(4)+(2)(-2)}&{(6)(1)+(2)(3)}&{(6)(0)+(2)(-2)}\\
{(-2)(4)+(3)(-2)}&{(-2)(1)+(3)(3)}&{(-2)(0)+(3)(-2)}\end{array}\right] \\=\left[\begin{array}{ccc}
{14}&{7}&{-2}\\
{20}&{12}&{-4}\\
{-14}&{7}&{-6}\end{array}\right]$
