Where does it say in the bible that the Universe is only 6,000 years old?

If I remember correctly its because the Bible lists the lineage from Adam and Eve. If you add up each of the ages listed eventually you come to events we know in history or other texts to cross reference. The idea goes that God created humans and within a few days either way the rest of the planet and all life, therefore if you know the age of Adam you can tell the age of the planet. Theres a little bit of guess work but the agreed average among Christians seems to be around 6000 years.

Just being general cos I couldn't be bothered looking up exactly which day.