What are some things that the government could offer for free?

I don't have a list for this, I am not a fan of government handouts beyond some minimal baseline. What I would offer here is providing education on how to do certain things related to financial literacy, how to take care of themselves physically (cut carbs, lift weights) and other forms of productivity that allows people to learn how to prevent/solve their own problems.

Key to this IMO would be to outsource the content outside of government personnel.

I'm thinking these would be several hours on an introductory level as opposed to something like weeks, months or a semester.