Is $\{12,18\} \cup ([-6,6] \setminus(-2,2))$ a compact set? Is the following set of real numbers compact?
$$\{12,18\} \cup ([-6,6] \setminus(-2,2))$$ 
It is obviously bounded (upper bound is $18$, lower bound is $-6$) but is it closed? I am not so familiar with topologic terms so please apologize if this question may seem a little dumb.

As general fact, if $A$ is closed and $B$ is open in a space $X$, then $A \setminus B$ is closed, because $A \setminus B = A \cap (X \setminus B)$, where $X \setminus B$ is closed as $B$ is open, and a intersection of two (or finitely many) closed sets is closed.
In your case you have a union of a compact set $\{12,18\}$ and a closed set $[-6,6]\setminus (-2,2)$. As the latter is also compact, as a closed subset of the compact set $[-6,6]$ you have a union of two compact sets, which is always compact.
