i want to get ibooks 3.1.3 for ios 6.1.6

If 3.1.3 was the last version compatible with iOS 6 then maybe by:

If you have iOS 4.2.1 or later on the iPod and there was version compatible with that version, then you should be able to get a compatible version by:

App Store: Downloading Older Versions of Apps on iOS - Apple Club

App Store: Install the latest compatible version of an app

You first have to download the non-compatible version on your computer. Then when you try to purchase the version on your iPod you will be offered a compatible version if one exists.

Otherwise you would have had to previously downloaded it and have it on your computer.