Answer
$B\cap E=\emptyset$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To get the elements of $
B\cap E
,$ get all the common elements of $B$ and $E$.
$\bf{\text{Solution Details:}}$
The intersection of $B$ and $E,$ given by $B\cap E$, is the set that contains all the common elements of $B$ and $E$.
With $
B=\{2,4,6,8 \}
$ and $
E=\{3,7\}
$ then
\begin{array}{l}\require{cancel}
B\cap E=\emptyset
.\end{array}