Tied up

A person who is 'tied up' is busy and can't take on a new request from someone else. It can also be used as an apology to say that they couldn't get to something they were supposed to be doing because something unexpected happened to prevent them from doing it. To add emphasis, they can say they're 'all tied up.' this expression is often used in a work place or other professional environment.

Example:
-I'm sorry; I can't help you with that. I'm all tied up today with a project. Maybe tomorrow?
-Sounds good.

-Did you finish the Stevens case?
-No, I'm sorry. I was all tied up in meetings with my team and never got around to it.

All tied up

If you're 'all tied up,' it means you're too busy to do whatever the other person is asking you to do. It's a typical expression you hear in an office.

Example:
-Can you go to lunch next Thursday?
-No, sorry. I'll be all tied up in court next week. How about the week after that?