to be very busy

I'd like to help, but I'm up to my neck at the moment. 我很乐意帮忙，但我这会儿正忙得不可开交。

to be very involved in a situation, or to have too much of the thing stated

She's up to her neck in debt/problems/work. 她债台高筑／问题缠身／工作繁忙。