Find the lateral area for the prism.

The area of the two bases, the triangles: (1/2)(4)(6)(2) = 24
The rectangle that faces toward the side: (4)(8) = 32
Now we need to find the width of the rectangle facing out toward us. We can do that by using the Pythagorean Theorem: 4² + 6² = 16 + 36 = 52. The width of the rectangle is √52, so the area of the rectangle facing toward us is 8√52 = 16√13
The area of the rectangle farthest from us: (6)(8) = 48
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We now have 24 + 32 + 48 + 16√13 = 104 + 16√13 inches².
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Hope this helps!