Final answer:
The medial pterygoid and lateral pterygoid muscles protract the mandible and enable side-to-side grinding of the teeth during chewing.
Step-by-step explanation:
The chewing muscles that protract the mandible and grind the teeth from side to side are the medial pterygoid and lateral pterygoid muscles. These muscles work in tandem to provide the necessary movements for mastication, or chewing. While the masseter is the main muscle used for elevating the mandible to close the mouth during chewing, the medial and lateral pterygoid muscles are responsible for the side-to-side grinding motions that help in breaking down food. The lateral pterygoid muscle, in particular, assists with the protraction or forward movement of the mandible.