Answer
$x^2+y^2 \leq 4$ and $0\leq z \leq 8$
Work Step by Step
"A solid cylinder...with center at the origin and radius 2" :
$x^2+y^2 \leq 2^2$ or
$y^2+z^2 \leq 2^2$ or
$x^2+z^2 \leq 2^2$
"lies on or below z= 8":
$z\leq 8$
and on or above the disk in the xy-plane:
$z \geq 0$ and $x^2+y^2 \leq 2^2$
Combine these rules to find:
$x^2+y^2 \leq 4$ and $0\leq z \leq 8$
