The correct answer is option 4: Rashtrakutas. The Rashtrakuta dynasty succeeded the Chalukyas in Western India.

Option 1, Cholas, was a powerful dynasty in South India, but they did not succeed the Chalukyas in Western India.

Option 2, Kakatiyas, was a dynasty that ruled over the Telangana region in South India and was not associated with Western India.

Option 3, Pallavas, was another dynasty that ruled over parts of South India, particularly the region of Tamil Nadu, and they did not succeed the Chalukyas in Western India.

Therefore, the correct answer is option 4, Rashtrakutas, who emerged as the successors to the Chalukyas in Western India.