We are designers and also a human being. Suppose I have problem at the same time i got a work from my favorite client. What can i do at the situation?

With regards to your problem either work related or not you still need to go to work since you got a work. With regards to your client either if he/she is your favorite or not you still need to see that client, because if you did not meet that client that will affect not just your reputation as professional but also the reputation of the company you are working with. Always look at the bigger picture that would result of your actions.

do not mix personal life with business handle your client proffetionallly