If you are getting the following error "itunes cannot sync apps to the iphone because the apps installed could not be determined" try the following:
1) Simply Restart your iPhone, to do so hold down the Top button and the Home button at the same time until the screen goes blank (or on older iPhones, you get a Slide to turn off screen).
2) Close down iTunes.
3) Turn your iPhone back on, and resync with iTunes.
This quick and easy fix, should hopefully solve the sync apps problem on your iPhone.