Find $f(f(f(4)))$ given $$f(x)=\begin{cases}\displaystyle{6^{x}+6}&\text{if}\ x \le 2\cr \displaystyle{6x^{5}-2}&\text{if}\ 2 < x \le 6\cr \displaystyle{3}&\text{if}\ x > 6\end{cases}.$$

$f(f(f(4)))=$

Hint: