This is the 10296th most frequent Russian word.
брачного
"Брачного" means "marital" or "pertaining to marriage."
Here, 'брачного' is an adjective formulated from 'брак' (marriage), modifying 'консультанта' (counselor) to describe the counselor who deals with marital issues.
Они искали брачного консультанта, чтобы спасти свой брак.
They were looking for a marriage counselor to save their marriage.
In this example, 'брачном' is used as an adjective in the prepositional case to describe 'контракте' (contract) related to marriage agreements.
Законы о брачном контракте меняются со временем.
The laws regarding a prenuptial agreement change over time.
Here, 'брачного' is an adjective modifying 'союза' (union) to specify that the union pertains to marriage.