How can you show someone that you’re really sorry

That's the only way. Apologize, and actions.

Buy them a car?

when my ex fucked up and he asked this and mention if i wanted him die ... i said yea.. he didnt , so no other way , well depending on what it is hopefully not that deep😅

Own the mistake, come clean and apologize at a level commensurate to the offense.

Sorry about what? Explain about what and they can believe you are

That is the most sincere way

Idk

you cant

Go down on them and don't stop.