The element is in set (A ∩ B) or set (A ∩ C) or both sets simultaneously.
Set A is present for both parts.
Therefore, this element is in set A.
We can use the distributive law to rewrite things a bit
(A ∩ B) ∪ (A ∩ C) = A ∩ (B U C)
Think of it like saying A*B + A*C = A*(B+C) where * represents set intersection and + represents set union.
Once we arrive at A ∩ (B U C), it should be more clear that the element must reside in set A.
It also resides in (B U C)
Meaning it's in B, or C, or both.
We'll shade the region in circle A that's either in B or C or both B & C.
Refer to the diagram that tutor @mananth had created to see what I mean.
.
(