At the end of The Outsiders, the greasers and Socs hold a "rumble," a big fight, which the greasers win. Afterward, Dallas takes Ponyboy to the hospital to see Johnny, who dies. Dallas is overcome with grief, and he runs away. Later he calls the gang for help because he has held up a store and the police are following him. When the gang runs out to meet Dallas, they see him get shot by the police.
Each of these incidents, the rumble, the death of Johnny, and the death of Dallas, can be read as climactic points in The Outsiders. If you need to do an assignment on this, it will be up to you to decide which is the main climax, and which are the sub-climaxes. Which, in your opinion, is the major plot line of the story? Is it the greater conflict between Socs and greasers, which gets resolved, at least for a short time, with the rumble? Or is it the personal plot about the relationships in Ponyboy's gang? If so, which friendship makes a greater impression on Ponyboy, the one with Johnny or the one with Dallas?