An example of courage is when George shoots Lennie in order to save him from law enforcement.
George travels with Lennie everywhere, taking care of him. Lennie is large and mentally challenged, and has trouble remembering things. George protects him, makes sure they stay employed, and tries to keep him out of trouble. He enjoys taking care of Lennie, because it is important to him to have someone to take care of. He even spins a yarn of a fantastic dream for him, involving saving up enough money to buy a ranch with rabbits (Lennie likes soft things).
When Lennie gets into trouble in Weed, George is able to help them recover and get another job. Soon, they know they are in danger when they see Curley’s wife and Curley. She is a tease, and he wants a fight. Lennie accidentally kills a puppy, and then makes a bigger mistake. Trying to touch Curley’s wife’s hair, he somehow breaks her neck. When George finds out what happens, he knows what he needs to do. As much as he cares for Lennie, he is a danger to society. Also, Lennie would not understand why he was in trouble, and being arrested and tried would be terrible for him.
"I should of knew," George said hopelessly. "I guess maybe way back in my head I did." (ch 5)
George does not think Lennie can survive alone after he runs away. He knows he has to go find him, and put him out of his misery. George finds Lennie hiding in the bush, like he told him to.
Lennie said, "I thought you was mad at me, George."
"No," said George. "No, Lennie. I ain't mad. I never been mad, an' I ain't now. That's a thing I want ya to know." (ch 6)
It took a lot of courage for George to shoot Lennie after taking care of him for so long, but he had to do it. He acts for the greater good, and for Lennie's best interest rather than his personal feelings. In shooting Lennie, he is destroying both Lennie's dreams and his own.