G-Drive external drive not showing up on my Mac

Since the files matter, don't erase or reformat anything, whatever Disk Utility suggests. In Disk Utility go to View > Show All Devices. You'll see the physical drive and the volume under it. Select the greyed out volume and click Mount. If that fails, run First Aid on the volume and then try Mount again. Before all that, swap the cable and plug it straight into the Mac, not a hub. Some G-Drives need their own power adapter too, and a drive that's short on power can show up half-recognised just like this. If First Aid reports errors it can't fix, stop there and look at recovery. Every extra repair attempt on a failing drive makes recovery harder.