what happens that gives Amir hope that Sohrab may someday be happy again? how does amir respond to this sign of hope?

Amir explains that four days earlier, a miracle happened. He and Soraya took Sohrab to an Afghan picnic in the park, along with Khanum Taheri. General Taheri was not there because he had finally gotten his wish; he had been offered a post in the Afghanistan ministry. By now, people had gotten used to Sohrab's silence and even Soraya could not bear trying to engage him anymore. Only Amir kept trying. Suddenly, Amir noticed kites flying over the park. He bought one and brought it to Sohrab. He told him that Hassan was the best kite runner he had ever known and asked Sohrab to fly the kite with him. Sohrab remained silent, but Amir knew what to do; he ran as fast as he could to launch the kite. As he stared up at it, he noticed that Sohrab had followed him and handed him the string. Sohrab soon gave it back to him. They stood in silence once more until they noticed a green kite closing in on theirs. When the kite came close enough, Amir performed Hassan's favorite kite-fighting trick, "the old lift-and-dive" as Sohrab watched, mesmerized. The green kite fell out of the air. When Amir looked down at Sohrab, he witnessed a half-smile steal over Sohrab's face. He asked, "Do you want me to run that kite for you?" Sohrab nodded, and Amir told him, "For you, a thousand times over." Amir ran among the children, after the kite.

When Amir and Sohrab fight the blue kite, the story finally comes full circle. The sport takes Amir back to the moment before everything changed, when Hassan had not been raped and they were just two boys having fun together. He says, "I was twelve again." Now that Amir has forgiven himself, kite fighting reminds him of pleasure instead of pain. His memories no longer being painful, he shares them with Sohrab: "Did I ever tell you your father was the best kite runner in Wazir Akbar Khan? Maybe all of Kabul? ... Watch, Sohrab. I'm going to show you one of your father's favorite tricks, the old lift-and-dive." In the ultimate moment of circularity, Amir runs the kite for Sohrab just as Hassan ran his last kite for him half a century before. Finally Amir understands what it is like to be as loyal and loving as Hassan, and can truthfully repeat Hassan's words, "For you, a thousand times over." The kite is a symbol of Amir's good, fatherly wishes for Sohrab. He wants to bring him joy, opportunity, a sense of security, and the will to live again, if only this were as easy as bringing him the kite. The last time Amir went to find a kite, he ended up turning his back on Hassan for good by running away from the scene of his rape. This is why the novel's last words, "I ran," are so meaningful. Even though Amir's story has made a circle metaphorically speaking, it has not ended where it began. Amir is running in a positive way, away from Sohrab physically but toward him emotionally. He is finally running with freedom in his heart instead of fear.

http://www.gradesaver.com/the-kite-runner/study-guide/section8/