Several important conflicts take place in chapters 6 to 8 of S.E. Hinton's The Outsiders.
In chapter 6, Johnny Cade and Dally come into conflict when Johnny tells Dally that he plans to turn himself in to the police for the murder of Bob. This is a significant moment in the novel because Johnny rarely speaks up, and he rarely takes a stand; he must feel very strongly about his decision to talk to Dally with such certainty. Also, Johnny looks up to Dally, so voicing a plan to do something that does not meet with Dally's approval also lends this conflict significance. Dally becomes emotional at the thought of Johnny going to jail and tries to persuade him to change his mind, indicating the depth of Dally's resistance to Johnny's plan.
In chapter 7, Ponyboy and his brothers come into conflict with the system. After Ponyboy comes home from the hospital, Steve drops by the Curtis house and discusses a newspaper article with Ponyboy. Ponyboy realizes with a shock that there is talk of the three Curtis brothers beings separated and that he and Sodapop might be forced to go into a boys' home. Ponyboy's dismay demonstrates the importance of his relationships with both of his brothers; he cannot bear the thought of living away from them.
In chapter 8, Johnny experiences a conflict with the nurse who tells him that his mother has arrived for a visit. His horrified response to the prospect of seeing his mother demonstrates the problematic nature of their relationship; seeing her would do Johnny more harm than good, which emphasizes Johnny's vulnerability.