en_tn/2ch/36/20.md

The king carried away to Babylon

Here "the king" refers to his soldiers whom he ordered to do the work. The phrase "carried away" is an idiom that means to forcefully bring them to Babylon. AT: "The king had his army forcefully take to Babylon" (See: rc://en/ta/man/translate/figs-metonymy and rc://en/ta/man/translate/figs-idiom)

until the rule of the kingdom of Persia

"until the kingdom of Persia came to power"