Q: i have lost an audiobook from my iphone how can i download it again

According to that article you can not redownload audiobooks like you would everything else

http://support.apple.com/kb/HT5085.

So in the future I would suggest to make sure you backup everything to the computer.

But in the meantime you can email itunes to regrant that book to you here.

http://www.apple.com/support/itunes/contact/

Click "contact itunes store support" and email about your book.