This is the 1030th most frequent Polish word.
państwowej
"Państwowej" means "state" or "national" (relating to the state or government).
In this sentence, 'państwowej' describes 'telewizji' (television), referring to the state or national broadcasting service.
Dostaliśmy zaproszenie na imprezę państwowej telewizji.
We received an invitation to the event organized by the national television.
Here, 'państwowej' modifies 'administracji' (administration), denoting that it pertains to the government or state authority.
Spotkanie odbyło się w sali państwowej administracji.
The meeting took place in the hall of the state administration.
Here, 'państwowej' is an adjective modifying 'uczelni' (university), indicating that the university is state-run or public.