Coordinate Geometry: JEE Main 2023 Mathematics question

The vertices of a hyperbola H are ($\pm$ 6, 0) and its eccentricity is ${{\sqrt 5 } \over 2}$. 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 _____________.