First compute h_{9}(x)
Given: h_{n}(x)=g^{n}(x) , g(x)= x+1
g^{2}(x)= g(g(x)) = g(x+1)=(x+1)+1 =x + 2*1
g^{3}(x)= g(g(g(x))) = g(g^{2}(x))=g(x+2)= (x+2)+1 = x+3 = x+ 3*1
Seeing this pattern we can infer that g^{9}(x) = x+ 9*1=x +9
So, h_{9}(x)=g^{9}(x)=x+9
Now we have to compute h_{9}^{8}(x) where x=72
h_{9}^{1}(x) = x+9
h_{9}^{2}(x) = h_{9}(h_{9}(x)) = h_{9}(x+9) = (x+9) +9 = x+2*9
h_{9}^{3}(x) = h_{9}(h_{9}(h_{9}(x))) = h_{9}(h_{9}^{2}(x))= h_{9}(x+2*9) = (x+2*9) +9 = x+3*9
Again following the same pattern we can conclude that
h_{9}^{8}(x) = x +8*9 =x+72
Put x=72 , it becomes 72+72=144