13 So the battle began. And the Syrians fled from Joab, and the Ammonites fled from Abishai.
18 David killed 700 chariot men and 40,000 horsemen.
19 After the battle, the Syrians made peace with Israel, and were afraid to help the Ammonites again.
A few more words about this episode
He also smote Moab. (8:2)
In 1 Samuel 22:3-4 while David was an outlaw, David asked the king of Moab to protect his mother and father and allow them to live in Moab. I guess now he's paying them back for their kindness.
Jonathan's son, Mephibosheth (9:4)
Mephibosheth's feet were permanently injured when he was five years old (2 Samuel 4:4) so he would be one of "the lame and blind" that are hated by David's soul (2 Samuel 5:8). So it's somewhat ironic that David would be kind to him now.
But maybe since Mephibosheth was the last surviving male descendant of Saul, and therefore had a claim to the throne, David wanted to keep an eye on him.
I'll be kind to Hanun, since his father, Nahash, was kind to me. (10:2)
Nahash was the Ammonite king who gave the people of Jabesh-Giliead that strange deal: I'll make a treaty with you if you let me poke out your right eyes. (Episode 105, 1 Samuel 11) That's all we know about him. But I guess because Nahash was an enemy of Saul that was enough for David to say Nahash was kind to him. (The enemy of my enemy is my friend.)