In the upcoming 6G era, vehicular networks are shifting from simple Vehicle-to-Vehicle (V2V) communication to the more complex Vehicle-to-Everything (V2X) connectivity. At the forefront of this shift is the incorporation of Large Language Models (LLMs) into vehicles. Known for their sophisticated natural language processing abilities, LLMs change how users interact with their vehicles. This integration facilitates voice-driven commands and interactions, departing from the conventional manual control systems. However, integrating LLMs into vehicular systems presents notable challenges. The substantial computational demands and energy requirements of LLMs pose significant challenges, especially in the constrained environment of a vehicle. Additionally, the time-sensitive nature of tasks in vehicular networks adds another layer of complexity. In this paper, we consider an edge computing system where vehicles process the initial layers of LLM computations locally, and offload the remaining LLM computation tasks to the Roadside Units (RSUs), envisioning a vehicular ecosystem where LLM computations seamlessly interact with the ultra-low latency and high-bandwidth capabilities of 6G networks. To balance the trade-off between completion time and energy consumption, we formulate a multi-objective optimization problem to minimize the total cost of the vehicles and RSUs. The problem is then decomposed into two sub-problems, which are solved by sequential quadratic programming (SQP) method and fractional programming technique. The simulation results clearly indicate that the algorithm we have proposed is highly effective in reducing both the completion time and energy consumption of the system.