The climax of Of Mice and Men is when Curley’s wife is killed, because Lennie’s death is the resolution.
The climax is the turning point of the story. It is the point where everything changes. Curley’s wife’s death is the climax because at that point the story cannot continue the way it was.
Before Curley’s wife died, the conflict was mostly between George and Lennie and the ranchers. George tries to protect and take care of Lennie, and avoid misunderstandings. Once Lennie kills Curley’s wife, this is no longer possible.
Lennie’s death is the resolution because it is George’s solution to the new problem the climax brought. The conflict is still the same, in some ways. Lennie is still a problem for George. However, the problem has gotten so bad that George’s only solution is to kill Lennie.
"Gonna do it soon."
"Me an' you."
"You... an' me. Ever'body gonna be nice to you. Ain't gonna be no more trouble. Nobody gonna hurt nobody nor steal from 'em." (ch 6)
We know George cares about Lennie because he shoots him to avoid his getting caught. He does not shoot until he hears the men coming, and he distracts Lennie with stories of rabbits.