i have purchased an audiobook from itunes. where do i find it on my iphone?

If your phone is on iOS 8.4 or 8.4.1 then it should have downloaded into its iBooks app - you should have an Audiobooks collection in the app.

If it's on an older version of iOS it should be in the Music app in the Audiobooks tab.

As audiobooks are a one-time only download from the store you may want to connect your phone to your computer's iTunes and do File > Devices > Transfer Purchases to copy it over so that you can take a backup copy of it.

I have tried syncing 3 times. It is not in iBooks. I have the most up to date version of iPhone for the 5.

Why did you make it so confusing? I spend an hour doing this every time i want to download a book!

We are fellow users, not iTunes Support nor Apple.

Does it show as being on the phone when connected to your computer's iTunes e.g. it shows in Audiobooks under the 'on my device' heading ?

And does the spotlight search screen on your phone find it ?