up to their necks vs up to my neck

up to their necks and up to my neck both are adjectives.

Word	Noun	Adjective	Verb	Adverb
up to their necks	No	Yes	No	No
up to my neck	No	Yes	No	No

As adjectives, up to their necks and up to my neck are synonyms defined as:

Other synonyms of up to their necks include neck-deep, up to her neck, up to his neck, up to our necks, up to your neck.

up to their necks (adjective)	up to my neck (adjective)
deeply involved	deeply involved