At the second temple's dedication, how many male goats were offered as a sin offering for all Israel?

Answer: Twelve

Along with 100 bulls, 200 rams and 400 lambs, they offered twelve male goats as a sin offering, one for each tribe of Israel.

“For the dedication of the house of God they offered a hundred bulls, two hundred rams, four hundred lambs, and a sin offering for all Israel of twelve male goats, one for each tribe of Israel.”— Ezra 6:17 (BSB)