#### Answer

The height of the box is 4 feet.

#### Work Step by Step

We know that the box has 6 faces. The surface area of the box, 496 ft^{2} is equal to the sum of the areas of each of the 6 faces. All faces are rectangular, so the area of a face is equal to the product of its two sides. Therefore, the top and bottom faces have an area of 18*8=144, the end faces have an area of 8h, and the remaining two faces have a length of 18h. Adding the areas of all the faces to equal the total surface area of 496 feet squared, this situation can be modeled by the equation 2*144+2*8h+2*18h=496, remembering that each face has an adjacent opposite face.
Solving for h in the equation:
2*144+2*8h+2*18h=496.
144+8h+18h=248. Divide both sides by 2
144+26h=248. Combine like terms
26h=104 Subtract 144 from both sides
h=4 Divide both sides by 26.
Therefore, the height of the box is 4 feet.