up to his neck vs up to her neck

up to his neck and up to her neck both are adjectives.

Word	Noun	Adjective	Verb	Adverb
up to his neck	No	Yes	No	No
up to her neck	No	Yes	No	No

As adjectives, up to his neck and up to her neck are synonyms defined as:

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

up to his neck (adjective)	up to her neck (adjective)
deeply involved	deeply involved