24-Hour Visa Free Transit

You will almost certainly fly with China Eastern and its subsidiary Shanghai Airlines and not with China Airlines :)

Never mind... Your itinerary is definitely eligible for 24 hour visa free transit and you do not need any kind of visa. However, you should be aware that you will have to be very quick at your first landing in China because upon your landing in Shanghai you will have to obtain a temporary entry permit to be allowed to cross the immigration because your next flight to Ningbo will be a domestic one. This is not a problem, but it might be somewhat time consuming. You should approach the area with immigration and have your flight plan (tickets) ready to be presented to relevant authorities. The best thing in this case is to have your itinerary printed out.

When your permit is granted, you will cross the immigration and run toward the gate for your flight to Ningbo. Since it will be a domestic one, there will be no immigration, but just a security. Upon landing in Ningbo, you will cross the security and the immigration because your next flight will be toward Hungary.

It should be fine, but remember, you should be very fast after your landing in Shanghai!