In a rectangular prism with a square base, two sides will be squares and 4 sides will be rectangles.
The dimensions of the squares are 6 x 6
The dimensions of the rectangles are 6 x h
Surface area is the sum of the area of each side of the prism.
The two squares each have an area of 6(6) = 36
The 4 rectangles each have an area of 6h
Since we know the total surface area is 264, let's put this together.
2(36) + 4(6h) = 264
72 + 24h = 264
Subtract 72 from each side
24h = 192
Finally, divide each side by 24.
h = 8
The height of the rectangular prism is 8".