a shipping box is shaped like a rectangular prism. It has a total volume of 96 cubid inches. The height is two inches less than the width and the length is eight inches longer than the width. What are the dimensions of the box?

Let the width be w. Volume=96=w(w-2)(w+8).
w³+6w²-16w-96=0=w²(w+6)-16(w+6)=(w²-16)(w+6). So the only positive root is w=4 inches.
The dimensions are 4” wide, height is 2”, length is 12”.