What is the largest volume if the surface area of the container is 96 m^2?

My work:

V = lwh

V = xyz

SA = 96 = xy + 2xz 2yz

z = (96 - xy)/(2x + 2y)

V = xy(96 - xy)/(2x + 2y)

V = (96xy - (x^2)(y^2))/(2x + 2y)

Not sure if my work is on track... But can somebody show me how to get the answer? It's x = y = z = 4m.