1. Imagine that this sentence is in the present tense: It IS at the American School ... that influences ... WILL interact, intermingle ... and so on. The sentence is looking at a future event from the perspective of the PRESENT. Thus, Present + Future.

2. The sentence that you have submitted begins in the past tense: It WAS at the American School. And the sentence is contemplating something that was going to happen later on at the American School. It is looking at a future event from the perspective of the PAST. In other words, it is thinking about THE FUTURE IN THE PAST. Since WOULD is the past form of WILL, the sentence must talk about this potential event by using WOULD before a bare infinitive. Thus, WOULD INTERACT, and so on.

3. WOULD applies to all the verbs in the sequence, and these must be parallel. Therefore, B is the correct answer. It WAS at the American School ... that influences ... WOULD INTERACT, INTERMINGLE, AND GIVE BIRTH. These three actions, from the perspective of the past, are potential actions, and their result in the past was what became (in other words, THE THING THAT BECAME) American Sign Language.

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