Carbon Dating is only accurate back ~50,000 years, so it is useless for dating materials from the dinosaur age (about 65 million years ago). Other elemental decay rates are used to determine dates for items older than the effective range of carbon-dating.
As to where creationists get their 6-10,000 year old number, that comes from two main sources.
1. The ages of people in Genesis, which states how old each generation was from Adam to Noah.
2. The geneologies of Luke and Matthew, which state every generation from Adam to Jesus.
From these two they work backwards to figure our the date of the flood, then backwards to Adam.
Generally, they arrive at 6,000 years ago, though through some wiggle room they can push that back as far as 10,000 years.
Far shorter than the 4.5 billion years old as the generally accepted age of the earth.