Respuesta :
Number 2 has an infinitive because it says offered to. Offered is a verb + to = infinitive.
The sentence that contains an infinitive is 2. Although she was busy, Clayton's mother offered to give him a ride.
An infinitive phrase contains a verb in its infinitive form after the preposition "to". In this case, the infinitive phrase is "to give".
Even though the sentences in the other options contain the preposition "to", the preposition is not followed by a verb in its infinitive form. The preposition "to" is followed by noun phrases like "the skate park", "her boss" and "his mother's car".