Sync button is greyed out in iTunes on my computer. How do I fix

Your question in the other discussion that you started received answers from two of us. Since you haven't given any indication of why our responses haven't helped you, all I can suggest is the following:

• connect your phone to your computer and select the iPhone icon once it appears on iTunes' top bar menu:

• the view should now show you the Device/Settings/Summary pane (1.)
• select the Device/Setting/Films pane (2.) Your iTunes may state videos, or movies, rather than films, dependant upon which language choice you originally chose:

• click on the Sync Films box (3.) and then either select the Automatically include option or select only the videos that you want from the list in 4. Until you do this, none of your videos have been selected to be synchronised with your phone
• Now tap the Sync (or Apply) button in the lower right corner of the iTunes window (not shown in the screenshots)

If you are still stuck, please indicate at which point in the suggested steps things don't do what you expect (and state what you expect to happen).