There are a couple of different external conflicts in Beverly Cleary's Dear Mr. Henshaw. The greatest external conflict concerns Leigh's difficulties in coping with his parents' divorce. He feels extremely sad and lonely, especially because he feels completely cut off from his father. As the book progresses, Leigh feels sadder the more his father breaks his promises to him; Leigh feels heartbroken to the point of thinking that his father doesn't really love him. Since Leigh is struggling so much with his father, we can call this an external character vs. character conflict, which is a conflict between two characters.
Leigh's external character vs. character conflict begins reaching its greatest point of intensity in early February of his sixth-grade year. That Christmas, Leigh received a gift from his father but didn't hear from him until the 8th of January. Though his father promised to call again in a week, Leigh doesn't hear from him for the rest of the month. Leigh begins feeling so lonely and desperate to hear from his father that, on February 4th, Leigh phones his father's trailer, not expecting his father to be home. The phone call is extremely upsetting to Leigh because he realizes his father actually was at home, sitting around not calling him. He also learns that his father lost Leigh's dog, Bandit, on the highway in a snowstorm. Worse yet, Leigh hears a strange boy asking, "Hey, Bill, Mom wants to know when we're going out to get the pizza?," which makes Leigh realize he is just not a part of his father's life anymore, making him feel unloved ("Sunday, February 4").
On top of Leigh's external character vs. character conflict with his father, Leigh is experiencing a second external character vs. character conflict at school because someone is bullying him by stealing from his lunch. Leigh feels that if his father were around, he would be able to handle the lunch thief better. Both character vs. character conflicts reach their climax when Leigh feels so angered by both his father and the lunch thief that he nearly kicks any random kid's sack lunch down the school hallway as an act of revenge. However, luckily, Leigh is stopped by Mr. Fridley, who tells Leigh he needs to stop being so absorbed with his own problems, start noticing everyone has problems, and start thinking positively.
Leigh resolves both character vs. character conflicts through positive thinking because positive thinking allows him to make friends, no longer care about who the lunch thief is, and to accept the fact his father will let him down. But Leigh also comes to realize that just because his father disappoints him doesn't mean his father doesn't love him. Leigh grows so understanding of his father's difficult job and loneliness that Leigh suggests his father keep Bandit once Bandit has been found.