Answer
(a) $$AB=\left[ \begin {array}{cc} 60&72\\ -20&-24
\\ 10&12\\ 60&72\end {array}
\right]
.$$
(b) $BA$ not defined.
Work Step by Step
Given
$$
A=\left[\begin{array}{r}{6} \\ {-2} \\ {1} \\ {6}\end{array}\right], \quad B=\left[\begin{array}{cc}{10} & {12 ]}\end{array}\right.
$$
We have
(a) \begin{align*}
AB&=\left[\begin{array}{r}{6} \\ {-2} \\ {1} \\ {6}\end{array}\right]\left[\begin{array}{r}{10} & {12 }\end{array}\right] \\
&= \left[ \begin {array}{cc} 60&72\\ -20&-24
\\ 10&12\\ 60&72\end {array}
\right]
.
\end{align*}
(b) $BA$ not defined.