Turning the king's heart represents making him think differently about the work of the temple. Alternate translation: "changed the attitude of Assyria's king" or "made Assyria's king willing" (See: [[rc://en/ta/man/translate/figs-metonymy]])
Strengthening their hands in the work represents helping them to work. The Assyrian king did this by telling them to do the work and providing the money for it. Alternate translation: "to help them do the work of his house" or "to make it possible for them to do the work of his house" (See: [[rc://en/ta/man/translate/figs-metaphor]])