Hello AAPL.

It is simple. You just have to eval f on 6 and the simplify. I will show you:

$$f\left(6\right)=\frac{6!+\left(6+1\right)!}{\left(6+2\right)!}=\frac{6!+7!}{8!}.$$

Now, we can write 7! and 8! as follows: $$7!=7\cdot6!\ \ \ \ \ \ and\ \ \ \ 8!=8\cdot7\cdot6!$$

Now, let's replace this on f(6). We will get

$$f\left(6\right)=\frac{6!+7\cdot6!}{8\cdot7\cdot6!}=\frac{6!\cdot\left(1+7\right)}{6!\cdot\left(8\cdot7\right)}=\frac{8}{8\cdot7}=\frac{1}{7}.$$

So, the correct answer is D.

I hope this help you.

Regards.