Question 1023100
Let w = width in inches, h = height in inches, and l = length in inches.
Without loss of generality, let 

wh = 12, 
hl = 24, and 
lw = 32.

The first two equations imply that {{{12/w = 24/l}}}
==> l = 2w ==> (2w)w = 32 after substitution into the 3rd equation.
==> {{{w^2 = 16}}} ==> w = 4 inches.
==> l = 8 inches, and h = 3 inches.

Therefore the volume is 3*4*8 = 96 cubic inches.