Answer
\[\mathbf{j}\]
Work Step by Step
\[\begin{align}
& \text{Let the vectors be: }\mathbf{u}=2\mathbf{k},\text{ }\mathbf{v}=4\mathbf{i}+6\mathbf{k} \\
& \\
& \text{Find }\mathbf{u}\times \mathbf{v} \\
& \mathbf{u}\times \mathbf{v}=\left| \begin{matrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
0 & 0 & 2 \\
4 & 0 & 6 \\
\end{matrix} \right| \\
& \mathbf{u}\times \mathbf{v}=\left| \begin{matrix}
0 & 2 \\
0 & 6 \\
\end{matrix} \right|\mathbf{i}-\left| \begin{matrix}
0 & 2 \\
4 & 6 \\
\end{matrix} \right|\mathbf{j}+\left| \begin{matrix}
0 & 0 \\
4 & 0 \\
\end{matrix} \right|\mathbf{k} \\
& \mathbf{u}\times \mathbf{v}=0\mathbf{i}+8\mathbf{j}+0\mathbf{k} \\
& \mathbf{u}\times \mathbf{v}=8\mathbf{j} \\
& \\
& \text{Finding a unit vector that is orthogonal to both }\mathbf{u}\text{ and }\mathbf{v} \\
& \frac{\mathbf{u}\times \mathbf{v}}{\left\| \mathbf{u}\times \mathbf{v} \right\|}=\frac{8\mathbf{j}}{\sqrt{{{\left( 0 \right)}^{2}}+{{\left( 8 \right)}^{2}}+{{\left( 0 \right)}^{2}}}} \\
& \frac{\mathbf{u}\times \mathbf{v}}{\left\| \mathbf{u}\times \mathbf{v} \right\|}=\mathbf{j} \\
\end{align}\]
