Coordinate Geometry: JEE Main 2023 Mathematics question

The foci of a hyperbola are $( \pm 2,0)$ and its eccentricity is $\frac{3}{2}$. A tangent, perpendicular to the line $2 x+3 y=6$, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the $\mathrm{x}$ - and $\mathrm{y}$-axes are $\mathrm{a}$ and $\mathrm{b}$ respectively, then $|6 a|+|5 b|$ is equal to __________