Set up the iterated integral for evaluating ${}_{D}f(r,,z)rdzdrd$ over the region $D,$ where $D$ is the solid right cylinder whose base is a region in the $xy-$plane that lies inside the cardioid $r=2+2cos$ and outside the circle $r=2,$ and whose top lies in the plane $z=6.$

Enter the correct limits of integration. Use increasing limits of integration.

$f(r,,z)rdzdrd$

$($Type exact answers, using $$ as needed.$)$