#### Answer

$\color{blue}{B \cap E = \emptyset}$

#### Work Step by Step

Given:
$B=\left\{2, 4, 6, 8\right\}$
$E=\left\{3, 7\right\}$
RECALL:
$B \cap E$, the intersection of sets B and E, is the set the contains the elements that are common to sets B and E.
Notice that sets B and E have no elements in common.
Thus,
$\color{blue}{B \cap E = \emptyset}$