**Explanation:**

The hill which deflects the Bay of Bengal branch of advancing monsoon to India is the Arakan hills.

**Arakan Hills:**

The Arakan hills are a range of hills located in the Rakhine State of Myanmar (formerly Burma). These hills act as a natural barrier for the Bay of Bengal branch of the advancing monsoon winds.

**Deflection of Monsoon:**

The Indian monsoon is a seasonal wind system that brings heavy rainfall to the Indian subcontinent. It is characterized by two branches - the Arabian Sea branch and the Bay of Bengal branch. The Arabian Sea branch moves towards the western coast of India, while the Bay of Bengal branch moves towards the eastern coast.

When the monsoon winds from the Bay of Bengal approach the eastern coast of India, they are deflected by the Arakan hills towards the northeast direction. This deflection occurs due to the presence of these hills, which act as a physical barrier and prevent the monsoon winds from advancing directly into the Indian subcontinent.

**Effect on Rainfall:**

As the monsoon winds from the Bay of Bengal are deflected by the Arakan hills, they travel along the northeastern coast of India and reach the states of West Bengal, Odisha, and parts of Northeast India. This deflection leads to heavy rainfall in these regions, as the moisture-laden winds are forced to ascend the hills and release their moisture.

On the other hand, the western coast of India, including the states of Maharashtra, Gujarat, and Kerala, receives less rainfall compared to the northeastern coast. This is because the Arabian Sea branch of the monsoon winds is not deflected by any significant geographical barrier and can directly reach the western coast.

**Conclusion:**

In conclusion, it is the Arakan hills that deflect the Bay of Bengal branch of the advancing monsoon winds towards the northeastern coast of India. The presence of these hills plays a crucial role in determining the distribution of rainfall in different parts of the country during the monsoon season.