"con tal de (que)" is roughly equivalent to "so that" or "in order to". It is commonly used in "He'll do anything to..." -type sentences: Underwood es capaz de todo con tal de acceder a la Casa Blanca. Possible translations of your sentence: He says yes to everything to make you shut up She'll say yes to anything as long as she gets you to shut up

It means that you are tell him yes, yes, yes because you don't want a headache. That's more polite option than Shut up! Fuck! You are giving me a headache. "Provided that you shut up, he tells you to everything yes."