In chapter 6 of To Kill a Mockingbird, Nathan Radley mistakenly believes an adult intruder, specifically a black man, was in his garden, which justifies his decision to fire his gun. This assumption reflects the prevalent racial bias in Maycomb. He doesn't suspect the actual intruders - Jem, Scout, and Dill. Miss Stephanie repeats Nathan's words, using his mistaken belief as an opportunity to make a racist joke, highlighting her tendency to mock others and the prevailing racism in their town.

In Chapter 6 of "To Kill a Mockingbird", two meaningful quotes address themes of gender roles and bravery. The first, "Scout, I'm tellin' you for the last time, shut your trap or go home--I declare to the Lord you're gettin' more like a girl every day!" illustrates early views associating femininity with cowardice. The second, "I--it's like this, Scout. Atticus ain't ever whipped me since I can remember. I wanta keep it that way," highlights Jem's courage and desire to maintain his father's trust.

The line in Chapter 6 that foreshadows the trouble Jem will have in leaving the Radleys' back yard is: "It was a tight squeeze for him."

The children have been sneaking round the Radley place, hoping to get a good luck at Boo through the window. In order to get into the back yard they've had to climb under a narrow fence. The fence is a tight squeeze getting in, as it will be when Jem gets his pants caught on it later.

In chapter 6, Jem sees the shadow of Boo Radley. The children believe it is Boo's shadow because of its demeanor, which matches Boo's shy and curious nature. If it were Nathan Radley, he likely would have reacted aggressively. The shadow appears as Jem, Dill, and Scout attempt to peek into the Radley house, prompting them to flee in fear.

Jem calls Scout "Angel May" in chapter 6 of To Kill a Mockingbird to tease her for protesting their plan to visit the Radley house, implying that she is being overly cautious or prissy. This nickname, suggesting she is acting like a "goody two shoes," provokes Scout because it challenges her tomboyish identity and her desire to be seen as tough and equal to the boys.

Chapter 6 of To Kill a Mockingbird explores themes of bravery and fear. The children demonstrate courage by attempting to see Boo Radley and later face fear when Nathan Radley fires a shotgun. Jem bravely returns to retrieve his pants despite the danger, fearing disappointing Atticus more than the Radleys. Dill also shows bravery by covering for Jem. The chapter highlights the children's evolving understanding of fear and courage.

In Chapter 6, Mr. Nathan Radley believes he shot at an intruder whom he identifies as a "Negro" in his collard patch. The children, Jem, Scout, and Dill, were actually the ones sneaking around the Radley property, and they narrowly escape being hit because Mr. Radley fired into the air. This misunderstanding underscores the racial tensions and assumptions prevalent in the setting of the novel.

Jem returns to the Radley place alone at the end of Chapter 6 to retrieve his pants, which got caught on the fence during their escape from Mr. Radley's gunfire. He fears getting in trouble with Atticus after lying about losing them in a game of strip poker. Despite Scout's protests and fear for his safety, Jem feels compelled to go back and recover them to avoid punishment.

In Chapter 6 of "To Kill a Mockingbird," Dill and Jem see "the lady" in the moon. They imagine her sitting at a dresser combing her hair. This whimsical image is a part of the children's imaginative world as they navigate their summer adventures in Maycomb.

At a basic level, Scout learns in chapter 6 of To Kill a Mockingbird that it is best to spy on Boo at night and, after their spying adventure is over, that it was foolish. However, Scout also learns on a deeper level that she will not always understand Jem and that honor can be more important than safety, even if she does not understand that at this time. 

In Chapter 6, Scout exhibits behavior considered unladylike for a Southern girl by engaging in boys' schemes and using strong language. She participates in Jem and Dill's plan to spy on Boo Radley, crawling under a fence and spitting on a gate to reduce noise. Scout also helps hoist Dill to a window and joins in their escape through a collard patch. She further defies expectations by remaining silent about their activities when questioned by adults.

Dill's question "Cross in it tonight?" in chapter 6 refers to asking if the image of a cross can be seen on the moon. This relates to traditional beliefs about perceiving various images, such as a lady or a man's face, on the moon's surface. Jem responds that only the lady is visible that night.

Mr. Avery is introduced in chapter 6 and is depicted as an elderly man who urinates off his front porch at night, much to the amusement of Scout and Jem. Mr. Radley's character is also expounded upon in chapter 6, when the children sneak into his backyard and he shoots his shotgun into the air. Mr. Radley is a racist who does not want any intruders in his yard. Eula May, Maycomb's leading telephone operator, informs Atticus that school has been canceled due to inclement weather (chapter 8). Cecil Jacobs's character is depicted toward the beginning, when he yells racist insults about Atticus to Scout, Jem and Dill (chapter 9).