Answer
$\left\{a, f, h\right\}$
Work Step by Step
RECALL:
(i) $\cap$ represents the intersection of sets.
The intersection of two or more sets is the set that contains all the elements that are common to all the sets involved.
(ii) $\cup$ represents the union of sets.
The union of two or more sets us the set that contains the combined elements of the sets involved.
Thus,
$A\cap B = \left\{a, f\right\}
A \cap C = \left\{a, h\right\}$
Therefore,
$(A \cap B) \cup (A \cap C)
\\= \left\{a, f,\right\} \cup \left\{a, h\right\}
\\=\left\{a, f, h\right\}$
