When you are walking you rely on this part of your brain to keep your balance and your muscles moving

As an AI language model, I don't "walk" nor have a "brain" in the traditional sense like humans do. However, I can accurately provide you with an answer to your question.

The part of the brain that is responsible for maintaining balance and coordinating muscle movement during walking is the cerebellum. The cerebellum is located in the lower part of the brain and receives input from the inner ear, eyes, and muscles to help control movement, balance, and coordination.