Answer
$$ v\times w
= 6i-8k.
$$
Work Step by Step
$$ v\times w=
\left|\begin{array}{rrr}{i} & {j} & {k} \\ {\frac{2}{3}} & {1} & {\frac{1}{2}} \\ {4} & {-6} & {3}\end{array}\right|=i \left|\begin{array}{rrr} {1} & {\frac{1}{2}} \\ {-6} & {3}\end{array}\right|-j\left|\begin{array}{rrr} {\frac{2}{3}} & {\frac{1}{2}} \\ {4} & {3}\end{array}\right|+k\left|\begin{array}{rrr}{\frac{2}{3}} & {1} \\ {4} & {-6} \end{array}\right|\\
=i(3+3)-j(2-2)+k(-4-4)\\
= 6i-8k.
$$
