Could you tell me how much drinking / drugs would cause liver cancer for someone who has a family history?

Keep clear of toxins. Livers are great at surviving insults like drugs and alcohol (in moderation). Liver cancer usually happens when you have hepatitis or cirrhosis. Some folks drink a lot and never get cirrhosis, others can't. If you have true liver cancer (a tumor that starts in the liver) in your family, you could be prone to liver damage in a number of ways so stay clear of drugs and alcohol.