Will the rear end of a 1985 honda 250 big red fit on to a 1986 honda 350 forman four-wheeler?

Highly unlikely without some serious fabrication. The engine size is different. The model is different. The year is different. About the only thing these have in common is that they are Honda. With ATVs very few parts will interchange between models. These are completely different models of ATV. Strike 1. The different models have different engine sizes. The different parts are engineered to deal with different amounts of horsepower and torque. Strike 2. Many times a manufacturer will make subtle but significant design changes during each model year. Even if these were the exact same model ATV it would not guarantee parts from a 1985 would fit a 1986. Strike 3. Therefore the only way of possibly knowing if the parts could interchange is if you could lay them both on the workbench side by side and take measurements of all the mounting locations, brackets, and machined surfaces.