Here is one way to root your LG P880 Optimus 4X HD.
Let me provide you with information on how to backup/restore your phone data.
If you have Windows PC, then follow these steps:
1) Download Wondershare MobileGo for Android.
2) Install MobileGo. Open the application.
3) Connect your phone to your PC via the USB cable that came with your phone.
4) Once MobileGo has detected your phone, select your phone (should be something
like LG MTP USB Device or something. It can be found on the sidebar.
5) Before clicking on "One-click Backup", go to Desktop and create a new folder.
Label it "LG P880 Backup Files".
6) Next, go back to MobileGo and click One-click Backup. Select all of the files that
7) The backup process might take a while (like maybe 30 minutes). You might like to
multitask on your PC or something to while away the time.
8) Once completed, close the window. Disconnect your phone from your PC. Now refer to the website I have pasted the URL there above.
As for Mac, I'm not so sure. You have to ask other users. Sorry 'bout that pal.
Hope this helped you. Do click on Like! Thank You.