smc

As $f(x)=cx/2x+3$, we can plug that into $f(f(x))$ and simplify to get $c^{2}x/2cx+6x+9=x$ . However, we have a restriction on x such that if $x=-3/2$ we have an undefined function. We can use this to our advantage. Plugging that value for x into $c^{2}x/2cx+6x+9=x$ yields $c/2=-3/2$, as the left hand side simplifies and the right hand side is simply the value we have chosen. This means that $c=-3\Rightarrow \boxed{-3}$.