From the graph find the number of solutions. The figure below shows the function $f(x)$ . 

How many solutions does the equation $f(f(x))=15$ have ?
$a.)\ 5 \\
b.)\ 6 \\
c.)\ 7 \\
d.)\ 8 \\
\color{green}{e.) \ \text{cannot be determined from the graph}}$
From figure $f(x)=15$ occurs at $x\approx \{4,12\}$ and
$f(x)=4$ occurs at $4$ points and $f(x)=12$ occurs at $3$ points.
so i concluded answer is option $c.$
I look for a short and simple way.
I have studied maths up to $12$th grade.

I don't think that it is obvious that there is a real number $\alpha$ such that $3\lt \alpha\lt 5$ and $f(\alpha)=15$. 
