Coordinate Geometry: JEE Main 2023 Mathematics question

Let the tangent to the parabola $\mathrm{y}^{2}=12 \mathrm{x}$ at the point $(3, \alpha)$ be perpendicular to the line $2 x+2 y=3$. Then the square of distance of the point $(6,-4)$ from the normal to the hyperbola $\alpha^{2} x^{2}-9 y^{2}=9 \alpha^{2}$ at its point $(\alpha-1, \alpha+2)$ is equal to _________.