Public transport:
The most sustainable way to reach the area is by train to Oberdrauburg (from Lienz or Villach) or to Hermagor (from Villach).
From Oberdrauburg or Hermagor, you can then take a bus to the town of Kötschach-Mauthen. From there, depending on the season and availability, there is the option to use a call bus or a taxi to the Plöcken Pass.
Details at - Nassfeld Mobility Info as well as Kärntner Linien Route Planner
By car:
From Hermagor via the B111 (Gailtal Road) or from Oberdrauburg via the B110 (Plöckenpass Road) to Kötschach-Mauthen, then continue towards the Plöcken Pass to the Plöckenhaus.