How does Eurymachus attempt to avert bloodshed?

Eurymachus attempts to avert bloodshed by appealing to Odysseus's sense of reason and offering reparations for the wrongs committed by the suitors. He argues that they acted under the influence of their desires and suggests that they would be willing to make amends to restore peace. Eurymachus tries to persuade Odysseus that violence is not the solution and that negotiation could lead to a more favorable outcome for all parties involved. His approach highlights a desire for mercy and the hope of reconciliation rather than conflict.