iTunes is an application that runs on computers. There is an iTunes Store application on mobile devices but iTunes 10.6.3 isn't something for a phone. The iPhone4 runs iOS. We need to know what it is exactly you are trying to update. If it is a computer we need to know exactly which model and what software it is running.
Get more information about your computer. Go to the Apple in the upper left corner of any window, then "About This Mac". Write down what it says about "version"and report that here. Now continue to "More Info..." Copy and paste the information here, but omit the serial number and Hardware UUID (if present).