Q: How do I transfer my music from my desktop itunes to my device when the "sync"option is greyed out ?

This article may help:

If iTunes doesn't recognize your iPhone, iPad, or iPod - Apple Support

or try the following:

1. Open Control Panel > Device Manager
2. Plug in your device
3. Locate Universal Serial Bus Controllers > Apple Mobile Device USB Driver
4. Right-click and select Update Driver Software...
5. Click Browse my computer for driver software
6. Browse to C:\Program Files\Common Files\Apple\Mobile Device Support\Drivers or
                   C:\Program Files (x86)\Common Files\Apple\Mobile Device Support\Drivers
7. Click Let me pick from a list of device drivers on my computer
8. Click Apple Mobile Device USB Driver
9. Click Next, then Close and exit Device Manager