JEE Main 2023 Mathematics question on Conic Sections

The vertices of a hyperbola H are $(\pm 6, 0)$ and its eccentricity is $\dfrac{\sqrt{5}}{2}$. Let N be the normal to H at a point in the first quadrant and parallel to the line $\sqrt{2}x + y = 2\sqrt{2}$. If d is the length of the line segment of N between H and the y-axis then $d^2$ is equal to __________.