Answer: Somos
Step-by-step explanation:
So all of these answer choices are verb conjugations of the verb infinitive ser, which means to be. Carmen y yo translates to Carmen and I which could also be phrased as we. The sentence is supposed to be translated as Carmen and I are studious, so you have to conjugate the verb infinitive ser to match the pronoun we. The conjugation for that is somos.
Hope this helps!!! :)