You made mistake in client service which can effect the work of all department. If you will inform you manager you will be fired. What should you do?

Inform the manager immediately, there might be time to correct the mistake, instead of covering it up until it is too late to fix, the problem might get worse and affect other aspects of the company. The mistake will always be traced back to the source, so there is no use in hiding it. At least, if you own up to your mistake, the manager might consider keeping you, and if it is not possible due to company standards, you will leave the company on better terms rather than being fired for covering up your mistake.

Well in this situation, the best thing to do is to be patient and calm, find a way on how to handle the mistake you have done by analysing the matter very diligently, apply the best solution. you may also focus on other job to impress your manager and that time you can refer to him the mistake you have done.

Apologize to client & try to Resolve your Mistake with help of Senior , after resolving bring this to Manager Notification..   

honestly is the first thing that entered into my mind. i believe that if it's an accidental mistake there should be a solution or immediate action that could resolve the problem. being in -charge, if i could resolve it on my level, i would. but nevertheless i will not hide it from my manager. mistake that is unintentional is forgivable. maybe my manager could help on his/her level. and if in case the problem is too big not be resolve.  

I would try to solve the problem and poinformowałbym supervisor.

Loyalty to the company is an important issue and I believe that the supervisor would appreciate it, and the fact that it was a mistake and not a deliberate action.

Just simple, we need to be patient and apologize to the client. Make sure that it wont happen again. Be resilient to handle mistakes. After the problem resolve, just inform your manager that you resolve the  situation and it is fine.

I would suggest to find out a way to resolve the issue, if you can do it on your own then make things right and then inform your manager about the incident. If you need his/her help and go with a plan to correct it. You can't hide from your mistakes better face it and bear the consequences. If your manager is a better manager then he will understand.