A coworker shows a boss a picture on my private Facebook page in which I am at work while not working and now I am wondering can I be fired for this?

You should repost this question in an employment law section, it doesn't really involve any intellectual property issues.  My best recollection from law school is that most people are employees-at-will (if you have an employee handbook, it probably mentions this) and can be terminated without cause (and without good cause). If you are part of a union, then it becomes something to discuss with them. You will get better answers from an employment attorney. I hope you are ok.