No, you should not put 2-cycle oil in your Honda EU2200i generator. The Honda EU2200i is a four-stroke engine generator, which means it requires four-stroke engine oil.
2-cycle oil is specifically designed for use in two-stroke engines, which have a different lubrication system than four-stroke engines. Using 2-cycle oil in a four-stroke engine can lead to improper lubrication, potential damage to engine components, and reduced performance.
To ensure the proper operation and longevity of your Honda EU2200i generator, it is important to use the recommended four-stroke engine oil as specified in the owner's manual. This will help maintain the engine's performance, protect internal components, and maximize the generator's reliability.