Can i fly to beijing from europe.use the 144 hour visa free stay..then fly to taipei and then fly to

Yes, Juan, you can use 144 hr free transit for the trip europe-beijing-taipei.

Yes thanks
But can i come.back from Taipei to Shanghai on a 144 hour visa then fly back to Europe??

You can also enjoy the 144 hr free transit for the trip from Taipei to Shanghai then to Europe.

Great Nancy fantastic...do you know this 100% sure??? Otherwise I will lose my next trip to China if i cannot comenin a second time

The China exit stamp that you get on way to Taipei means you have officially left china. That means you are welcome to return again for 144 hour another transit without visa. Just make sure Shanghai is the only place in China where the planes stop (even if just for fuel)