Success!
I successfully rooted my LG P880 4X HD with the following software version and process. Please bear with me this is my first post on xda.
Software Version:
Android Version: 4.1.2
Baseband version: L6260_MODEM_SIC_02.1233.00
Kernel version: 3.1.10
Build Version: JZ054K
Hong Kong Software Version: P88020b-HKG-XXX
Process:
1. Downloaded and extracted "j794_root.rar" from this thread.
2. Turned off my phone and waited five seconds.
3. Held down the power button and volume down button simultaneously to enter "Android system recovery".
4. Once in "Android system recovery" I connected my phone to my pc with a mirco usb cable.
5. Then I scrolled to the option "apply update from ADB" with my volume rocker and selected it by pushing the power button momentarily.
6. A prompt came up saying, 'Now send the package you want to apply to the device with "adb sideload <filename>"'.
7. I then ran the file "root.bat" in the "J794_root" folder on my pc and the phone began the root process.
8. Once it said "Install from ADB complete." I selected "reboot system now" and my phone started up fine.
9. I checked my app drawer and now I have the superuser app installed.
There are a couple of photos attached to this post. One shows my software information and the other is a picture of the "Android system recovery" post rooting. You can see the different steps that took place during the root in that photo.