Q: Hi I bought audiobook last night but cannot find it anywhere in my itunes library when I go check for available downloads it says all downloads are up to date for this account when I go to buy audio book it says you have already purchased it so where is i

We are fellow users here on these forums, you're not talking to iTunes Support - I've asked the hosts to remove your phone number from your post.

Did you buy it on one of your devices or on your computer's iTunes ? It should have downloaded onto whichever device/computer that you bought it on, so on an iOS device it should be in the Music app, and if you bought it on your computer's iTunes then it should be in the Books part of your library. If you can't find it on what you downloaded it on, and you hadn't copied it off, then you can try contacting iTunes Support and see if they will let you redownload it - you can either contact them via http://reportaproblem.apple.com , or  you can try contacting iTunes support via this page : http://www.apple.com/support/itunes/contact/ , click on Contact iTunes Store Support on the right-hand side of the page, then Purchases, Billing & Redemption