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  164 square inches

Step-by-step explanation:

You can compute the area by adding the areas of the 4 corner triangles, the 4 side rectangles and the central square.

The area of the triangle is ...

  A = (1/2)bh = (1/2)(4 in)(4 in) = 8 in²

The area of a rectangle is ...

  A = LW = (6 in)(4 in) = 24 in²

The area of the central square is ...

  A = s² = (6 in)² = 36 in²

Then the total area is ...

  4(8 in²) +4(24 in²) +36 in² = (32 +96 +36) in² = 164 in²

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Alternatively, you can draw a 14-inch square around the whole figure, then subtract the areas of the four corner triangles that are not part of the octagon. The area computed that way would be ...

  (14 in)² - 4((1/2)(4 in)(4 in)) = 196 in² -32 in² = 164 in²