How many hours do you work for game designing

It depends. If you are freelance then you would most likely be working for no pay until the games release, so you would be working your own hours. That would mean one of two things. Either A: you would be working a tiny bit each day maybe to hours, or B: You would be working as much as possible and sometimes work 24 hour days.
On the other hand if you are employed by a company then you are only allowed to work the standard full time schedule. Most employed game devs. work full time.