Step 2. Download and Install Latest Motorola Drivers from below .
Step 3. Go to Moto G 3rd Gen Settings > Developer Settings and Select Allow OEM Unlock .
Step 4. Switch off your Motorola Moto G 3rd Gen and Boot to Fastboot mode by pressing Power + Volume down button at the same time .
Step 5. Now Open Minimal ADB and fastboot ( which you downloaded in step 2 ) on PC and open cmd from there .
Step 6. Connect your Motorola Moto G 3rd Gen to PC via USB cable .
Step 7. Type This on Cmd fastboot oem get_unlock_data .
You will get a String , just copy it and Paste it in a Notepad and remove empty spaces from it .
Step 8. Go to Motorola's website and Log in using your Google / Motorola Id and paste the Copied String on 6th Step .
Step 9. Now complete all the Steps at Motorola's Website and Request unlock key .
Step 10. You will get an Unlock key at your mail id , just copy it .
Step 11. In Cmd ( which you opened following step 5 ) type -
fastboot devices
It will check , your device is connected or not , after that type -
fastboot oem unlock Key
Replace Key with the Unlock Key , you got on Step 10 .
Downloads -