Be as busy as a bee 非常忙
Can we meet next week instead? I’m as busy as a bee right now.
All the new toys kept the kids occupied for hours.
Have one's hands full 很忙
I have my hands full with all these meetings today, so can I call you back tomorrow?
Be tied-up 很忙的，脱不开身的
I'm afraid we can't meet till Wednesday - I'm tied up on Monday and Tuesday.
Have a lot on (one's) plate 很忙
I just have a lot on my plate right now while I'm finishing up my degree and doing this huge project for work.