Jamieson, Fausset and Brown on Zechariah 6:8

8. north ... quieted ... my spirit--that is, caused My anger to rest (Jud 8:3, Margin; Ec 10:4; Eze 5:13; 16:42). Babylon alone of the four great world kingdoms had in Zechariah's time been finally punished; therefore, in its case alone does God now say His anger is satisfied; the others had as yet to expiate their sin; the fourth has still to do so.

Zec 6:9-15. Ninth Vision. The Crowning of Joshua.

The double crown is placed on Joshua's head, symbolizing that the true priesthood and the kingdom shall be conferred on the one Messiah. Compare He 6:20; 7:1-21, on Melchisedek, who similarly combined the kingdom and priesthood as type of Messiah.