Answer
$\left\{a, e\right\}$
Work Step by Step
RECALL:
(1) $\cup$ represents union of sets. The union of two sets is a set that contains the combined elements of the two sets.
(2) $\cap$ represents intersection of sets. The intersection of two sets is a set that contains all the elements that are common to the two sets.
To find the elements of the given set, you have to (i) find the union of $A$ and $B$, then (ii) find the intersection of $A\cup B$ and $C$ afterwards.
Note that:
$A \cup B =\left\{a, b, c, d, e, f\right\}$
Thus,
$(A \cup B) \cap C
\\= \left\{a, b, c, d, e, f\right\} \cap \left\{a, e, g\right\}
\\= \left\{a, e\right\}$
