I would write:
$\displaystyle \vec{A}\cdot\vec{B}=\langle 4,2 \rangle \cdot \langle x,y \rangle=4x+2y=-16\,\therefore\,2x+y=-8$
Now, since $\displaystyle \vec{B}$ and $\displaystyle \vec{C}$ are perpendicular, to what will we equate their dot product?