This is the 11149th most frequent Russian word.
государственном
"Государственном" means "state" or "governmental" in English, referring to something related to the government or state.
Here 'государственном' is used as an adjective modifying 'учреждении', meaning 'state'. It describes the type of institution as being part of the government or public sector.
Он работает в государственном учреждении.
He works in a state institution.
In this case, 'государственном' refers to the 'budget' and characterizes it as pertaining to the operations or finances of the government.
Вопрос о государственном бюджете был обсужден на совещании.
The issue of the state budget was discussed at the meeting.
Here, 'государственном' describes 'управлении', indicating that the lecture relates to the governance or administration of the state.