Question 415899
he box has a volume of 16 cubic feet.
L * W * H = 16
: 
The width should be 2 feet less than the height.
W = H-2
:
 The length should be 4 feet greater than the height.
L = H+4
:
Replace L and W in the 1st equation
(H+4) * (H-2) * H = 16
FOIL
(H^2 - 2H + 4H - 8) * H = 16
:
H(H^2 + 2H - 8) = 16
:
H^3 + 2H^2 - 8H - 16 = 0
No integer solution for this, plot it on your trusty graphing calc
y = x^3 + 2x^2 - 8x - 16

{{{ graph( 300, 200, -6, 5, -10, 10, x^3+2x^2-8x-16) }}}
Find the positive solution using the 0 feature
x = 2.8284
so we have
L = 6.8284
W = 0.8284
H = 2.8284
:
You can confirm this by finding the vol using these values