What ray is a common side of ∠EOB and ∠BOA?

The ray OB is in common to the angles EOB and BOA.

To solve this problem, you need to determine what rays each angle has and what ray is in common to both angles.

Angle EOB has two rays. They are

ray OE

ray OB

Angle BOA also has two rays. They are

ray OB

ray OA

Looking at the available rays, the only ray in common to both angles is ray OB. So the answer is ray OB.