In iBooks app, after signing in with your AppleID and password, tap 'purchased'...
Edit to add... sorry - read the headline as iBooks not audio books...
In iTunes, the Audio Books section should behave just like Music, TV Shows, Movies... on the iTunes Store app, in the bottom right... tap "More"... you should see a Purchased link somewhere you can tap... then you can select from your purchases and Family member purchases if you've set up a FamilyShare... and if you've set up FamilyShare in less than the past 24 hours, give it an overnight to process and make family member purchases visible to the rest of the family group.