392 in square
You break the figure into two.
Bigger prism, l=6, h=10, w=6
Smaller prism, l=6, h=4, w=4
There are 10 sides to this shape, one side from big figure and one side from small figure overlap.
Big figure
4(l•h)=4(6•10)=4•60=240
2(l•h)=2(6•6)=2•36=72
Small figure
2(l•h)=2(6•4)=2•24=48
2(l•h)=2(4•4)=2•16=32
Shape
240+72+48+32=392 in^2