Young Earth Creationists claim the Earth is about 6,500 years old according to Earth's clock. Keep in mind this doesn't mean they believe that other parts of the universe are this age too. Gravity effects how fast a clock runs so other parts of the universe may be much older.
Carbon 14 dating is actually a friend to the young Earth belief. Diamonds, dinosaur bones, and coal have all been dated to less than 50,000 years. In fact, based on Carbon's decay rate, anything that contains Carbon must be less than about 60,000 years old. But the key to remember on any dating method is that it is built upon assumptions that cannot be verified. These assumptions are accepted on faith.
Take the below linked article that discusses how the sun can impact carbon in the atmosphere, which in turn effects how much carbon is contained in tree rings. The article states, "When the activity of the sun changes, it has direct effects on the earth. For example, when the sun is relatively inactive, the amount of a type of carbon called carbon-14 increases in the earth's atmosphere. Because carbon in the air is absorbed by trees, carbon-14 levels in tree rings actually reflect solar activity and unusual solar events in the past.".
So you can see here that carbon levels in the atmosphere DO fluctuate and so the amount of carbon originally put into something can and does vary. What are some other assumptions? The speed at which elements leave an object and the rate of decay in different environments are just a couple more. Whenever you see dating of millions of years, you must know this is not a fact, but an interpretation based on their faith assumptions and religion.