let me know

The phrase "Let me know ___" means "Tell me ___". It's extremely common in everyday English, because "Tell me ___" can sound too demanding or angry.

Here are some examples:

Let me know when you're free and we'll set up a meeting.

Let me know when you hear from them.

If you encounter any problems, please let me know immediately.

You can see "Let me know..." a lot in business emails.

(something) works

When something "works", it means that the people you're speaking or writing to think it's OK.

For example:

A: I'm free this Wednesday after five. Does that work?

B: Yeah, that works for me.

This expression is very common in business communication. It seems more confident than asking if something is "OK":

Let me know if that's OK with you.

This is something you might write to an executive in your company or to a customer who you've only spoken with a few times before.

Let me know if that works for your team.

This is something that you'd write to a coworker or client who's somewhat equal to you in status, or who you know well.