Final answer:
Nestor wanted Agamemnon to apologize to Achilles and offer him compensation to regain his support and participation in the war.
Step-by-step explanation:
In the Trojan War, Nestor, the oldest among the Greek chieftains, blamed Agamemnon for the Greeks' loss and wanted him to take action to resolve the issues caused by his quarrel with Achilles. Nestor wanted Agamemnon to apologize to Achilles and offer him compensation to regain his support and participation in the war. He believed that without Achilles, the Greeks would continue to struggle in the war against the Trojans.