Answer
$A\cap C= \{ a \}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To get the elements of $
A\cap C
,$ get all the common elements of $A$ and $C$.
$\bf{\text{Solution Details:}}$
The intersection of $A$ and $C,$ given by $A\cap C$, are all the common elements of $A$ and $C$. With $
A=\{ a,b,c,d \}
$ and $
C=\{ a,e,f,g \}
$ then
\begin{array}{l}\require{cancel}
A\cap C= \{ a \}
.\end{array}