jmc

Let the roots of the cubic be $r$, $s$, and $t$. We are given that ${\log }_{2}r+{\log }_{2}s+{\log }_{2}t=4$. Using a property of logarithms, we can rewrite the equation as ${\log }_2(rst)=4$, or $rst=2^4=16$. Notice that this is just the product of the roots of the given polynomial. The product of the roots is also equal to $-\frac{a}{9}$. Thus, we have $-\frac{a}{9}=16$ and $a=\boxed{-144}$.