Answer
$a=0.144=18/125$
Work Step by Step
Because $a$ is directly proportional to $m$ and $n^2$, and inversely proportional to $y^3$, we can expressed $a$ by this equation:
$a=\frac{kmn^2}{y^3}$
Then, replace $a$, $m$, $n$, $y$ with the value given would yield us the constant k.
$9=\frac{k*4*9^2}{3^3}$
$9=\frac{k*4*3^4}{3^3}$
$9=k*4*3=12k$
$k=3/4$
Now, we are able to use this $k$ value to find the missing $a$ with a different set of $m$, $n$, $y$ given.
$a=\frac{3/4*6*2^2}{5^3}=\frac{3*6*4}{4*125}=72/500=0.144$