I'm going to assume that this is a plastic storage bin. I googled those dimensions and the only terrarium with an 8" height that I found was a critter keeper. I searched for storage bins and found some 56 quart storage bins that had those approximate dimensions.
I kept an adult male bp in a 48 quart bin for a year, before it started injuring itself by pushing. So, I'd guess you've got until he's about 36 - 40 inches. When I got my bp, he was an adult, so I don't have a guess as to how long it will take for your bp to reach that length.