jmc

We have that $A+B+C+D=36$. Substituting everything in terms of $C$, we find that $(2C-2)+(2C+2)+C+(4C)=36$, which means that $C=4$. Thus $A=6$, $B=10$, and $D=16$. Therefore our desired answer is $6\cdot 10\cdot 16\cdot 4=\boxed{3840}$.