Digital Twin (DT) has emerged as an enabling technology for the 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 to transform the DT capabilities into the 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: (1) Strengthening the human-machine interaction via driving behavior analysis; (2) Improving the traffic safety via knowledge-based vehicle fault diagnosis; (3) Analyzing the spatial-temporal traffic characteristics via data aggregation. Furthermore, we investigate two case studies for illustrating how the DT capabilities can be utilized to perform the 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.