How many satraps did Darius appoint to rule throughout his kingdom?

Answer: 120

Darius set 120 satraps over the kingdom, with three administrators over them, Daniel being one.

“Now it pleased Darius to appoint 120 satraps to rule throughout the kingdom, and over them three administrators, including Daniel, to whom these satraps were accountable so that the king would not suffer loss.”— Daniel 6:1-2 (BSB)