In the present world, transportation systems prioritize sustainable growth strategies to minimize costs, carbon emissions and vehicle maintenance in logistics and supply chain management. The focus lies on integrating efficient route planning with preventative maintenance and optimization techniques. A few studies on multi-objective four-dimensional transportation problems have been done with type-2 uncertain variables, but no one has formulated a multi-objective four-dimensional transportation problem with normal type-2 uncertain variables. Also, no available study incorporates vehicle and road-specific constants when considering model formulation with maintenance costs and carbon emissions. The proposed model fills this gap by integrating these constants, thereby enhancing their realism within the transportation sector. This paper studies a multi-objective, green, four-dimensional transportation problem to demonstrate how managers can reduce the cost of vehicle maintenance and carbon emissions by carefully choosing the route and the vehicle. The model parameters have been taken to be normal type-2 uncertain variables as these variables provide a more nuanced representation to handle higher levels of uncertainty for accurate modeling and analysis than the other uncertain variables. Critical value-based optimistic, pessimistic and expected value reduction methods have been proposed to convert normal type-2 uncertain variables to type-1 uncertain variables. Chance measure and the generalized credibility programming has been used to transform the transportation parameters into the deterministic form. The results obtained are compared and analyzed in detail using different criteria. A sensitivity analysis was performed on the objectives to facilitate informed decision-making.