Find the surface area of the composite figure.

The easiest way to  do this is to first  find the surface area  of both figures

Surface area  of  larger figure  =

2 ( 8*2  + 14*8  + 14*2]  =   2 [ 16 + 112  + 28]  =  2 [ 156]  =  312 cm^2

Surface area of smaller figure  =

2  [ 8*4  +  6*4  + 8*6]  =  2 [ 32 + 24 + 48]  =  2 [ 104]  =  208 cm^2

From this  we want to  subtract the area of two  8 x 4 rectangles  [the areas  where each of the two objects are touching each other =  2 x 32  =  64 cm^2

So.....the total surface area  = 

[ 312 + 208  -  64 ]  =   456 cm^2