I have another idiom today which is often used in business situations: “to be tied up”. This expression is used when people want to say that they are busy doing other things so that they can’t do something else. For example:
I’m afraid I can’t meet with you on Monday at 3:00. I’ll be tied up all Monday afternoon.
I’m going to be tied up with meetings all day on Thursday. Let’s try to meet on Friday instead.
I’m sorry, but Mr. Tanaka is tied up in a meeting right now. Would you like to leave a message for him?
So, as I mentioned already, this expression is used in business situations. If you want to talk about a free time situation, you can say, “I’m busy.” or “I have plans”.