I know GFB is similar to CHB, but how do you find GF?

By AA similarity, △GFB is similar to △CHB, just as you said 

This means we can make the following equation:

GF / FB  =  CH / HB

                                      Now we can substitute  6  for  FB,  24 for  CH,  and  18  for HB

GF / 6   =   24 / 18

                                      Multiply both sides of the equation by  6

GF   =   (24 / 18)  *  6

                                      Simplify the right side of the equation

GF   =   8

Now we can find the area of  △GFB

area of △GFB   =   (1/2) * FB * GF   =   (1/2) * 6 * 8   =   24

We can see that because the left side of the big triangle is symmetrical to the right side, △GFB is congruent to  △DEA. (We can also say that since  m∠GBF = m∠DAE,    m∠GFB = m∠DEA,   and  DE = GF,  by AAS,  △GFB ≅  △DEA)

This means the area of △DEA is also 24 sq cm

Now we can find the area of △ABC.

area of △ABC  =  (1/2) * AB * CH  =  (1/2) * (2 * 18) * (24)  =  432

Now we can find the area of CDEFG.

area of CDEFG   =   area of △ABC  -  area of △GFB  -  area of △DEA

area of CDEFG   =   432  -  24  -  24

area of CDEFG   =   384   (and that is in sq cm)

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So CHB = CHA (triangles are similar)

So we can just find FHCG and multiply by 2. 

CHB = 24*12/2 = 144

GFB/CHB = 6/24

So CHFG = 108

108*2 = 216

=^._.^=