The Amara-Nayaka system was a significant political innovation implemented by the Vijayanagara empire. This system involved the appointment of military commanders or Nayakas to govern specific regions. The Nayakas were responsible for maintaining law and order in their territories and collecting revenue for the empire. This decentralized approach allowed the Vijayanagara empire to efficiently administer its vast territories and ensure effective governance.

Option 1: The Cholas were a powerful dynasty in South India but did not implement the Amara-Nayaka system.

Option 2: The Chalukyas were rulers in different parts of India but did not introduce the Amara-Nayaka system.

Option 3: The Guptas were an ancient empire in North India, known for their administrative advancements, but they did not implement the Amara-Nayaka system.

Option 4: The Vijayanagara empire is the correct answer as it introduced and implemented the Amara-Nayaka system as a major political innovation.

Alert - correct answer should be Option 4: Vijayanagara.