Digital Twin (DT) has emerged as an enabling technology for sixth generation (6G) vehicle-to-everything (V2X) communications. However, there are two crucial issues on leveraging DT for 6G V2X communications. First, what kind of DT capabilities can be combined with the 6G V2X networks? Second, how can we transform the DT capabilities into practical V2X network performance gain? Motivated to solve these problems, this article investigates the DT capabilities under a DT and mobile edge computing empowered 6G V2X network architecture. Specifically, three DT capabilities are presented: First, strengthening the human-machine interaction, via driving behavior analysis; second, improving traffic safety via knowledge-based vehicle fault diagnosis; and third, analyzing spatial-temporal traffic characteristics, via data aggregation. Furthermore, we investigate two case studies for illustrating how to utilize DT capabilities to perform task-efficiency oriented V2X network scheduling. In the first case study, the driver behavior analysis result is combined with the V2X channel scheduling strategy. In the second case study, a deep reinforcement learning-based vehicle merging decision is devised in the DT domain. Then, a coalition-based V2X channel scheduling strategy is proposed, to help accomplish the vehicle merging decision task. Finally, we evaluate the performance of our proposed task-efficiency oriented V2X channel scheduling schemes, and highlight the future research directions.