Win someone’s goodwill or favor.
“A great political stump-speech propitiates the voter base —more wall, anyone?”
“He tried to propitiate the judge but it backfired.”
I found it easy to misuse Propitiate, so it’s worth mentioning the other forms of the word that are more fun:
Noun: “The way he hangs around her is an obvious propitiation: She’s way out of his league.”
“My professor is easily propitiated by short skirts in the front row.”
— Those short skirts are propitiations, while the professor is propitiable, and the girls wearing the skirts are propitiators.