Answer
(a) see prove.
(b) $0\lt x\lt 18$
(c) $1728$
Work Step by Step
(a) The height of the box is $\frac{144-8x}{4}=36-2x$ and the volume is
$V=x^2(36-2x)=2x^2(18-x)$
(b) Let $18-x\gt 0$ we have the domain as $0\lt x\lt 18$
(c) The graph shows that the maximum happens at $x=12in, V=1728in^3$