The hero falls in love with a countess who is very beautiful.

adverb clause

infinitive phrase

past participial phrase

elliptical clause

adjective clause

The answer is: adjective clause.

An adjective clause provides further description of the noun or pronoun it modifies. It contains a relative pronoun or adverb, a subject and a verb. In the example sentence, the adjective clause is "who is very beautiful," which modifies the noun "a countess."

The rest of the options are incorrect because adverb clauses function as adverbs and add information concerning how, where, when, why or under what condition the action happens; infinitive phrases require an infinitive verb with to; past participial phrases need a past participle verb and elliptical clauses contain a missing part - usually a verb.