Éodir then speaks and the tensions does indeed seem to release somewhat. Héastan smiles, "Another young boy with princely words. You do know how to be polite at least. I tell you what, you best my in a flyting, and I will go with you to Edoras and see what justice is served. Lose and then face my justice? How does that offer sit with you?"
As he speaks, it becomes quite apparent that his men are quite uncomfortable, knowing that their leader would have them slay their fellow countrymen, and yet bound to him by loyalty.
But here Héastan sits, having challenged you to a flyting and awaiting your response. The flyting is an ancient tradition among the people of Rohan. Usually flyting is a peaceful contest. For a feast, the laughter and applause of the hall would tell the winner, who would win only renown and then share a cup with the loser. But in wartime, flyting often comes before a battle, as a fighter challenges the enemy and taunts one, perhaps a particular rival, to come forward and fight. And even in peacetime, some flytes go too far and lead to violence. You can tell that Héastan intends this to lead either to your humiliation or to rally him men to attack you.
You can agree to this battle of words and wits or else attempt to dissuade him.