I just found out that one of my twins has died (i am at 12 weeks). Will this cause a problem for my other baby?

Condolences for your. Loss. As sad as the day is there is a possibility that the remaining twin can carry on & deliver. Close monitoring by your OB will be important. You need to understand that you may still go into labor early or face other pregnancy complications. A good sit down discussion with your OB may clarify specific issues about your case that only the two of you know.
Probably not. This is more common than people realize. This happened relatively early in the pregnancy so the effects on the other baby should be minimal.