Answer
The function has an absolute maximum equal to $24$ and an absolute minimum equal to $-8.$
Work Step by Step
$g'(x)=4x-8.$
$g'(x)=0\to x=2$ which is in the specified interval; hence, it is, along with the endpoints of the interval, a possible candidate for absolute extrema.
$g(0)=0.$
$g(2)=-8.$
$g(6)=24.$
The function has an absolute maximum equal to $24$ and an absolute minimum equal to $-8.$
