how to downgrade iphone 4s from io6 to ios 5.1.1 ..

You can't downgrade

Downgrading iOS - Unsupported

I'm sorry, but Apple does not provide a downgrade path for iOS. That said there is a way to downgrade, but it's not supported by Apple, and it's done at your risk.

Start by downloading the iOS firmware file required for the iOS version to which you want to downgrade. You will find them at Download iOS firmware for iPhone iPad iPod. Be extremely careful to select the correct IPSW file for the iDevice model you have and the desired version of iOS. I cannot stress enough that installing the wrong firmware can brick your device.

After downloading your iOS IPSW file I suggest putting it on your Desktop. Connect your device to your computer and open iTunes. You should see your device listed under the Devices heading in iTunes' sidebar. Select your device then click on the Summary tab in iTunes' main window. You should see a section titled, Version, with two buttons: Check for Update and Restore.

I highly recommend that you perform a sync/backup before proceeding. This will assure that when the device is restored you can restore the most recent backup. Otherwise, you will lose all your files, apps, and data.

Press and hold down the OPTION key on the keyboard then click on the Restore button. This will open an Open dialog. Navigate to the Desktop where you have the IPSW file, a file ending with an ."ipsw" extension. Select the ".ipsw" file then click on the Open button. The rest should be pretty much automatic. Except instead of restoring the current firmware, iTunes will restore the firmware in the ".ipsw" file.

Again, I cannot stress enough that installing the wrong firmware can brick your device. Be sure you have your device connected to a charger.