This is the 12322nd most frequent Russian word.
кабинету
The Russian word "кабинету" is the dative case of "кабинет," meaning "to the office" or "to the study."
The word 'кабинету' in this sentence is the dative case form of 'кабинет', indicating the indirect object of the verb 'подошел' (approached), referring to the office of the principal.
Я подошел к кабинету директора.
I approached the principal's office.
In this case, 'кабинету' shows possession or location associated with the preposition 'в', denoting something belonging to or situated within the office.
Чехлы на стульях в кабинету выглядят новыми.
The seat covers in the office seem new.
Here, 'кабинету' is used after 'в', relating to the locative context of the action described, referencing the office's interior.