This one wants us to evaluate the following limits of this exponential function.
$$\lim_{x \to \infty} \frac6{e^x-6}$$
I'm not sure how to approach this problem. I did easily figure out this version of the problem when x approached negative infinity.
On
All of the parts of the function are continuous where defined, including at $-\infty$ and $+\infty$, so you can just plug in $x = +\infty$.
If you aren't comfortable with the extended real numbers, going through the exercise of plugging in $x = +\infty$ should at least give a hint about what's going on.
Intuitively, when $x \to +\infty, e^x \to +\infty$, so the whole thing goes to zero. Can you make that more precise?