How do you go about doing this surface area problem?

Break it down into 2-Dimensional shapes. Then add the areas together.

From the picture you can see;
front & back rectangles are 2*(4 x 8) = 64 m²
2 side rectangles are 2*(4 x 12) = 56 m²
2 triangular front & back pieces are (1/2)*8*3 = 12 m²
2 roof rectangles are 2*(5 x 12) = 120 m²

total Surface area = 64 m² + 56 m² + 12 m² + 120 m²
= 252 m²

For the volume; break it up into 3-dimenssional shapes and add the volumes together.

From the picture you can see;
Rectangular box volume is 4 x 8 x 12 = 384 m³
Triangular roof volume is area of front triangle multiplied through the length. (1/2)*8*3* 12 = 144 m³

Total volume = 384 m³ + 144 m³
= 528 m³