Consider that the figure is composed by six parts, two of them are squares with side 4 in and the other parts are rectangles with length 6 in and height 4 in.
The total surface area is the sum of two times the area of the square and four times the area of the rectangle:
AT = 2(A1) + 4(A2)
A1 is the area of the square:
A1 = 4x4 in² = 16in²
A2 is the area of the rectangle:
A2 = 4x6 in² = 24 in²
Next, replace the previous values into the expression for AT:
AT= 2(16 in²) + 4(24 in²)
AT = 32 in² + 96 in² = 128 in²
Hence, the total surface area is 128 in²