Q. The line $x=8$ is the directrix of the ellipse $E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with the corresponding focus $(2,0)$. If the tangent to $E$ at the point $P$ in the first quadrant passes through the point $\left(0,4\sqrt{3}\right)$ and intersects the $x$-axis at $Q$, then $(3PQ)^2$ is equal to _____ .