In Chapter 9 of "To Kill a Mockingbird," the Finch family gets together with Atticus's brother Jack for Christmas dinner. Scout's cousin Francis tells her that his grandmother is going to teach him to cook; Scout scoffs at this statement, saying that "boys don't cook." Then, when Scout mentions that she does not want Dill to wait on her after they are married, Francis ridicules Dill, calling him a "runt." They argue, and Francis tells Scout,
You're mighty dumb sometimes, Jean Louise. Guess you don't know any better, though.
When Scout asks him what he means, Francis replies,
If Uncle Atticus lets you run around with stray dogs, that's his own business, like Grandma says, so it ain't your fault. I guess it ain't your fault if Uncle Atticus is a nigger-lover besides, but I'm here to tell you it certainly does mortify the rest of the family--
Francis goes on to say that Grandma says that Atticus is letting the family down. Rising and sprinting far enough away, he yells, "He's nothin' but a nigger-lover!" To this Scout runs and "collars" him, but Francis yells the insult again, running into the kitchen. So, Scout waits for the opportunity for him to come back out, but Francis calls to his grandmother that Scout is keeping him from coming out. With confidence after Scout is scolded, Francis emerges and go outside. Softly he hurls the invective again. But, this time Scout punches him in the teeth, skinning her hand. Uncle Jack pins her arms while Grandma wipes away Francis's tears while Scout gets a spanking from Uncle Jack.
This chapter marks a difficult time for Scout as she has had to answer to insults about her father both at school and in her home environment. And, she is beginning to learn how easily people are influenced by others when they do not think for themselves.
The passages that you are looking for are in chapter 9 of the book. Scout, in typical Scout style, practically beats Francis up. Granted, Francis pretty much asked for it by baiting her, but still. The situation is that Francis, who Scout doesn't like one bit to start off with (she says of him that he ""was the most boring child I ever met"), calls Atticus a "nigger-lover" not once, but three times. Scout, who has been asked by her father in the previous chapters to NOT fight anyone who says something mean about him, patiently waits until Francis is within arm's reach and
"split [her] knuckle to the bone on his front teeth...[then] sailed in with [her] right,"
flailing and punching Francis. So, the disaster is that Francis gets a whooping by Scout, and Uncle Jack has to intervene and pull the two apart. It kind of ends the festivities, and Scout gets in pretty big trouble over it with Uncle Jack and Atticus. It is a rather amusing disaster, as far as disasters go, but still, Scout was taught a valuable lesson about keeping her temper.
Francis basically gets beat up by Scout because he said some rude things about her father. Because of this she flew into a rage and decided to hit him. Her father before has told her NOT to fight with people, but she simply could not handle this. However, she waits until he is close enough and then hits him.