Answer
The vector is $\frac{7}{5}\mathbf{i}-\frac{21}{5}\mathbf{j}$.
Work Step by Step
The vector is
$\frac{2\left( -2 \right)+4\left( -6 \right)}{{{\left\| \mathbf{w} \right\|}^{2}}}\mathbf{w}$
The magnitude of $\mathbf{w}$ is
$\begin{align}
& \left\| \mathbf{w} \right\|=\sqrt{{{\left( -2 \right)}^{2}}+{{\left( 6 \right)}^{2}}} \\
& =\sqrt{4+36} \\
& =\sqrt{40}
\end{align}$
Substitute the value of $\left\| \mathbf{w} \right\|$ and $\mathbf{w}$ in the above equation to get
$\begin{align}
& \frac{2\left( -2 \right)+4\left( -6 \right)}{{{\left( \sqrt{40} \right)}^{2}}}\left( -2\mathbf{i}+6\mathbf{j} \right)=\frac{-28}{40}\left( -2\mathbf{i}+6\mathbf{j} \right) \\
& =\frac{7}{5}\mathbf{i}-\frac{21}{5}\mathbf{j}
\end{align}$
