"A virtuous and good person neither quarrels with anyone, nor, so far as he can, does he allow anyone else to quarrel." (v. 1, p. 245)
Epictetus points to Socrates as the exemplar as he settled many quarrels and how patient he was in dealing with other people, including his wife and son. (see v. 3, p. 245) He was able to do this because "he kept the thought firmly fixed in his mind that no one can exert control over another person's ruling centre." (v. 4, p. 245) He knew he could never change other people, but rather he focused on "attending to his own business alone in such a way that others too" would see his example and want to also act according to nature (v. 5, p. 245) And for a person "in this state of mind" there is no "room left for contention." (v. 8, p. 245)
You can keep the peace and minimize quarreling by putting things in the proper context.
EVENT: "That man abused you"
RESPONSE: "I'm most grateful that he didn't hit me"
EVENT: "But he has gone on to hit you"
RESPONSE: "I'm most grateful that he didn't kill me"
This line of thinking is not unlike the teaching of Jesus when he instructed his disciples to "turn the other cheek" (see Matthew 5:38-40).
Some may think this reasoning is a bit extreme by today's standards. Indeed, if someone hits you, there are avenues to pursue to seek justice and these avenues allow people to pursue justice dispassionately and Stoicly.
What ought to matter to the individual human? Certainly not possessions and fame and distinguished appointments and careers. Bur rather, it ought to be how the individual manages her impressions and "imprints" that are borne in her mind. (v. 15, p. 246) And what imprints do her judgments carry? "Gentleness, sociability, patience, love of her neighbor" and not "quick to anger" or "prone to rage" nor being "discontented with her lot." (v. 17-18, p. 246-247)
There is no need to worry about what other people think of you. For their part, they are focused on wealth, health, prestige and fame. But your craft is to focus on being a good human being - someone who is concerned about exercising the appropriate virtue (wisdom, justice, courage, self-discipline) in any given circumstance. Beyond that, nothing else should matter to you. So, "why worry about them? Any more than a craftsman worries about people who have no knowledge of his craft." (v. 22, p. 247) In this way, you can settle quarrels and not start them.
And when people try to read your mind or try to "trigger" a reaction in you, then you should "come forward to proclaim that you're especially amused by [them] who imagine that they're able to harm you." (v. 24, p. 247) Similarly, "inhabitants of a well-fortified city laugh at those who are besieging them: 'Why are those men going to all that trouble to no purpose? Our walls are secure; we have provisions that will last for a very long time, as will all the rest of our supplies.' That is what renders a city secure and impregnable, and in the case of a human mind, it is nothing other than it's judgements." (v. 25, p. 247)
In a word, focus on strengthening your mind - on becoming mentally tough - and don't let possessions, wealth, health and fame drive your life. These are the "puppet strings" you must cut.
"It is a person's judgement alone about each thing that harms him, and upsets him, and this is what gives rise to dissension, and civil strife, and war." (v. 28, p. 248)
This is your task: "to adopt an attitude" that "no tyrant can hinder [you] ... nor can any master, nor can the crowd hinder [you], nor can the stronger hinder the weaker, because this has been granted to us by God free from all hindrance. These are the judgements that bring love into a household, and concord into a state, and peace among nations; and cause a person to be grateful to God, and confident at all times." (v. 34-35, p. p. 248-249)