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The solid figure has six sides: two squares and four rectangles. Figure out the area of each, add them together, and you've got the total surface area.

You can get the area of the six sides by doubling the area of each (8 by 8) corner and multiplying the area of the 8 by 12 rectangle by four. Here goes.

The squares contribute 2 * (8 * 8) = 128 square inches. The rectangles contribute 4 * (8 * 12) = 32 * 12 = 384 square inches. The total area of these surfaces is therefore 128 + 384 = 512 square inches.

Please let me know if you need any clarification. I'm always happy to answer your questions.

Jun 2nd, 2015

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