Correct answer is: B. Rabi-ul-Awai
The Islamic month associated with the Prophet Muhammad's migration (Hijrah) from Mecca to Medina, a pivotal event that started the Islamic calendar, is Muharram, the first month, though the actual journey began in late Safar and concluded in Rabi' al-Awwal, the third month. Muharram marks the start of the year of the migration, while Rabi' al-Awwal saw the Prophet's arrival in Medina.