Mathematics Question from JEE Main 2023 · 1 February, Shift 2

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 _____.