If 'god' didn't want people to think the world was 6,000 years old, why say it was in the book?
No such age of the earth is given in the Bible. ~6000 years is generally accepted as time span between the time that Moses received the Torah from God on top of Mount Sinai to this day, although that is not explicitly mentioned either. As for the "created in 6 days" description in Genesis, bear in mind in 2 Peter 3:8 we are taught that God's idea of a day is not our literal 24 hour day. It can be that, it can be a time span of indefinite length, or it can be an instant. Essentially, the Creation story is not on the same time scale as we are used to.
As other Christians have chimed in, the notion that the entire universe is 6000 years old is a view held by a minority of people who call themselves "Christian," even though they openly preach something that isn't Biblical. They are no more authoritative or sincere in their teachings than the Westboro "Baptist" "Church" is. And yes, I used that comparison on purpose because I believe the "young earth" crowd is in the same boat as the WBC crowd, after all, the results are the same.
Of course, spreading the idea that it is a mainstream Christian belief that the entire universe is 6000 years old does help to make Christianity look silly, which is why this argument is always propped up by non-Christians.