Walkthrough of Dragon's Dogma 2: Phantom Cart

To begin this quest, return to Vermund after completing the main quest. You can start the mission by talking to any NPC, but an easier way is to find the two NPCs at the cart station in the west of Vernworth. They discuss the ghost carriage and after their conversation the mission will begin. You can also approach the carts crossing the bridge to the northwest from Vernworth to activate the mission.

The ghost carriage only appears at night, so you'll have to head to the outskirts of town after sunset. Rest at the Wernworth Inn until nightfall, then take the northeast road to the junction with the other main road. When you reach the intersection, you will see a stopped cart, which will trigger a cutscene and begin this exciting quest.