I want to make a large sliding door based on a single sheet of 3/4″ plywood. The problem is, the sheet would ideally be 6 foot x 8 foot. I understand that the standard size is 4×8. Do 6×8 sheets exist ...

A standard sheet of plywood is 4'x8' and weighs anywhere from 25 to 85 pounds, depending on the thickness. The dimensions make a sheet awkward to carry by yourself, even if you can handle the weight.