The idiom "fall by the sword" means that they will die in battle. This can be stated in active form. AT: "their enemies will kill them with swords" or "their enemies will kill them in battle" (See: [[rc://en/ta/man/translate/figs-idiom]] and [[rc://en/ta/man/translate/figs-activepassive]])
Here the word "hand" refers to power. AT: "I will enable the king of Babylon to conquer all of Judah" (See: [[rc://en/ta/man/translate/figs-metonymy]])