$f(x)$
mean that the function $f$
is applied to $x$
, and $f^n(x)$
mean $f(f(...f(x)))$
, that is $f$
is applied to $x$
, $n$
times. Let $g(x)=x+1$
and $h_n(x)=g^n(x)$
. What is $h_n^m(0)$
?

What is
$g^n(x)$
in terms of$x$
and$n,$
and how does that relate to the function$h$
? 
How about trying to first find an expression
$h^2_n(x)$
? 
By trying values of
$m,$
give an expression for$g_n^m(x).$

We have
$h_n(x)=g^n(x)=x+n$
since$1$
must be added$n$
times. To compute$h_n^m(0)$
we may first obtain$h_n^m(x),$
and then evaluate it at$x=0.$
Consider that$h_n^2(x)=h_n(h_n(x))=h_n(x+n)=x+2n.$
We can hence inductively see that$h_n^m(x)=x+mn.$
Therefore$h_n^m(0)=mn.$