No, "four bedroom" is not an adjective. It's a noun phrase functioning as a modifier of the noun "house". The phrase consists of the determinative "four" + the noun "bedroom".
Nouns accept a very range of modifiers, including of course adjectives, for example:
Attributive modifiers
a long letter (adjective) another two candidates (determinative) a brick wall (noun) a sleeping child (verb)
Post-head modifiers
the tree by the gate. (preposition phrase) people fond of animals.(adjective phrase) the opera Carmen (appositive noun) a rug this colour (noun phrase) the guy who spoke first. (finite clause) students living on campus (non-finite clause)
(A cautionary note: some 'Mickey Mouse' grammar books and websites call everything that modifies a noun an adjective. That is of course ridiculous, and such ideas have no place in serious grammar.)