How did Odysseus recognize the good omen of Zeus?

Odysseus recognized the good omen of Zeus when he observed two eagles fighting in the sky, a sign interpreted by the seer Halitherses as a message from the gods. This omen indicated that Odysseus would return home and reclaim his place, reinforcing his resolve and the support of the gods in his journey. The event symbolized divine favor and foreshadowed his eventual triumph over the suitors in Ithaca.