I assume that your tagline saying that your Mac is on 10.4.8 is wrong as iTunes 12.3.3 requires 10.8.5+ - or is it the iTunes version that you say is installed is wrong ?
If your Mac has iBooks on it (OS X 10.9+) you can add the PDF to that via File > Add To Library, and it should then show (assuming that you aren't using iCloud Drive for iBooks on your phone) on the phone's Books tab for selecting and syncing to it - if it's on OS 10.8 add it to your iTunes library so that it shows for syncing.
Or you could email it to yourself and use 'open in' in the Mail app on your phone to add it to its iBooks app