Mixing car synthetic oil and motorcycle synthetic oil in motorcycle with wet clutch?

Look on the back of the bottle of the automotive oil. There should be a white circle that says the weight of the oil (eg. SAE 10W-30). If it says "Energy Conserving" in the bottom of that circle, it means that the oil contains friction inhibitors. It is not advised that you use this kind of oil in a wet clutch system because the clutch needs friction to operate and long term use may damage the clutch.

Most automotive oils labeled for high mileage vehicles do not have these friction inhibitors and may be used in motorcycles as long as they are still the right weight.