The formula should read SA=2lw+2lh+2hw.
96=2(lw+lh+hw); lw+lh+hw=48; l(w+h)+hw=48 has many solutions, so I guess you're looking for integer solutions?
Start with l=1 and let w=h: 2h+h^2=48; h^2+2h=48; h^2+2h+1=49; (h+1)^2=7^2 so h+1=7 and h=w=6. Therefore we have the dimensions (1,6,6) as the set of three dimensions. We can also have l=4 and w=h: 4(w+h)+hw=48; h^2+4h+16=48+16=64; (h+4)^2=8^2; h+4=8, h=w=l=4; (4,4,4) is a cube.
Also l=11 and h^2+22h=48; h^2+22h+121=48+121=169 giving us h=w=13-11=2 and (11,2,2) as the dimensions.
SOLUTIONS: Dimensions are 1', 6', 6' or 4' cube or 11', 2', 2'.