(one's) hands are full
Someone is too busy or has too much going on to be able to do or become involved with anything else. I really wish that I could babysit for you tonight, but I'm afraid my hands are full at the moment. Normally I'd pass a project like this on to Dave, but his hands are quite full this month. Hey, can you answer the door? I'm taking the roast out of the oven, so my hands are full.
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