Answer
$V(x)=4x^{3}-64x^{2}+240x, 0\lt x\lt6$
Work Step by Step
Length of box = $20-2x$
Width of box = $12-2x$
Height of box = $x$
Volume = Length$\times$Width$\times$Height
=$x(20-2x)(12-2x)$
=$4x(10-x)(6-x)$
=$4x(x^{2}-16x+60)$
=$4x^{3}-64x^{2}+240x$
$\because$ All lengths are positive,
Length = $20-2x\gt0, x\lt10$
Width = $12-2x\gt0, x\lt6$
Height = $x\gt0$
$\therefore 0\lt x\lt6$
