The correct answer is C) The Romans invaded Judea and forced the Jews to scatter.
The event that caused Yohanan ben Zakkai to start a school for rabbis was the Roman invasion of Judea which forces the Jews to scatter.
When the Romans invaded his city, Zakkai talked to Roman General Vespasian. He told Vespasian that he had a dream in which he saw Vespasian becoming the Emperor of Rome. After he told him about the prophecy, Zakkai asked Vespasian to let him have a school for rabbis to teach the Tora in Yavneh. Vespasian told him that if the prophecy was true, he would allow him to do so. One year after, Vespasian became emperor and he allowed Zakkai to have his school.