$8$
23. As shown in the figure, in the Cartesian coordinate system, the line $y=\frac{4}{5} x-4$ intersects the $x$-axis and $y$-axis at points $A$ and $B$, respectively. The fixed point $C$ has coordinates $(0,6)$, and point $M(a, 0)$ is a point on the ray $O A$ to the right of point $A$. A line $M N \perp C M$ intersects the line $A B$ at $N$, and $B M$ is connected. If the area ratio of $\triangle A M N$ to $\triangle A M B$ is 3:2, then the value of $a$ is . $\qquad$