Which of the following routes involves trade outside of the byzantine empire?

massilia to carthage

rome to athens

alexandria to ravenna

antioch to ephesus

The option would be the first one: Massilia to Carthage. We know this because Massilia to Carthage would have been partly outside of the empire. Carthage was part of the empire in North Africa, but the city of Massilia (today known as Marseilles) in what would become southern France was not. Hope this can help a lot