Answer
$\left[\begin{array}{ccc}
{14}&{7}&{-2}\\
{20}&{12}&{-4}\\
{-14}&{7}&{-6}\end{array}\right]$
Work Step by Step
C is a 3 by 2 matrix. B is a 2 by 3 matrix.
CB is defined and is a 3 by 3 matrix,
the entry $[CB]_{ij}$ = (row i of C)$\times$(column j of B)
$CB=\left[\begin{array}{ll}
4 & 1\\
6 & 2\\
-2 & 3
\end{array}\right]\left[\begin{array}{lll}
4 & 1 & 0\\
-2 & 3 & -2
\end{array}\right]$
$=\left[\begin{array}{ccc}
{4(4)+1(-2)}&{4(1)+1(3)}&{4(0)+1(-2)}\\
{6(4)+2(-2)}&{6(1)+2(3)}&{6(0)+2(-2)}\\
{-2(4)+3(-2)}&{-2(1)+3(3)}&{-2(0)+3(-2)}\end{array}\right]$
$=\left[\begin{array}{ccc}
{14}&{7}&{-2}\\
{20}&{12}&{-4}\\
{-14}&{7}&{-6}\end{array}\right]$