Step 1 - Download Root_with_Restore_by_Bin4ry_v13.zip to your computer and extract the zip file anywhere in your computer.
Step 2 - Connect your Xperia P to your computer using the USB cable. Make sure USB debugging is ON as given on the first page.
Step 3 - Also make sure all USB drivers are properly installed for your phone.
Step 4 - Go to the extracted files folder (in Step 1) and run the batch file ‘RunMe.bat‘.
Step 5 - Follow all the on-screen instructions and your phone will be rooted in 5 minutes.
NOTE: Your phone might restart 2-3 times during the process. It’s alright and no need to panic.
That’s it! Your Xperia P LT22 is now rooted on Android 4.0.4 ICS firmware! Check for the superuser app in your apps list to verify.Download SuperSu app from GooglePaly and update SU binery.
To make sure you have correctly installed the above root method and it’s working,verify with Root Checker as given in the link.
*Do it at your own risk.