An open box is formed from a rectangular piece of cardboard whose length is 8cm more than its width by cutting squares of 2cm from each corner and folding. if the volume = 256 what are the dimensions?

If the width of the cardboard = x cm then its length is given by x + 8 cm.
Then the length of the box will be x + 8 - 2(2) =  x + 4
and the width = x - 2(2) = x - 4 cm The height is 2 cm 

Volume = h*w*l = 2(x - 4)(x + 4) = 256
2(x^2 - 16) = 256
x^2 - 16 = 128
x^2  = 144 
x = 12 cm 

Dimensions of the box are:-

length =  12 + 4 =  16cm
width = 12 - 4 = 8 cm
height = 2 cm