Let $A\left(\frac{3}{\sqrt{a}},\sqrt{a}\right),a>0$, be a fixed point in the $xy$-plane. The image of $A$ in $y$-axis be $B$ and the image of $B$ in $x$-axis be $C$. If $D\left(3\cos \theta ,a\sin \theta \right)$,  is a point in the fourth quadrant such that the maximum area of $∆ACD$ is $12$ square units, then $a$ is equal to _____

Hence, the correct answer is 8.