You have an 8'board, cut off 3/4 for a shelf. You give 1/3 to your brother, how long is the piece you gave your brother?
I think you want to give your brother 1/3 of what is left over right? You need the 3/4 for your shelf.
If that is the case. 3/4 of 8 = 6
you take 6' for yourself and there is 2 feet left over and you will give your brother 2/3 ft.
If it means that you give your brother 1/3 of your shelf then the answer would be 2 feet.