I have a question

what does up to their necks mean?

[Snowcake]

People can be very busy, when they are up to their neck in work. There's a lot of work to be done.

Or

She is up to her neck in problems, which means there are many problems she has to cope with.

The construction of this idiom is

to be up to one's neck in something.

and it is used for negative and unpleasant situations.

Regards,
Snowcake