Answer:
Mariana y yo vamos manejar a New York.
Step-by-step explanation:
In this exercise, you have to choose the most appropriate infinitive verb for the context of this sentence. First, you have to look at grammar. In this case, all the verbs except for "seguir" could be used in this sentence because they collocate with the preposition "a" before an adverbial of place: doblar a algún lugar, cruzar a algún lugar, manejar a algún lugar. The verb seguir is not used with the prepostion "a" before an adverbial of place. "Seguir a" is used to indicate that somebody is following sb/sth, so this option must be discarded.
Once you have analyzed grammar, you have to look at meaning. As New York is a city, "doblar or cruzar a New York" does not make sense. It is more logic to drive to New York. Therefore, manejar is the correct answer.