Can I upgrade from iOS 6.0.1 to iOS 8.1.1 directly?
The iPad 2 will run iOS 8.1.2. However, if the storage is full it will not be able to install the update.

Connect your iPad to your computer and open iTunes. Check the iPad's storage. If there is less than 5 GB free space, delete movies, music or larger apps until there is space (you can reinstall easily after the update).

From iTunes, click "Update". iTunes will download the proper update from Apple and do everything necessary.

If it still complains, do this:

While connected to iTunes, click "Backup". When it finishes, disconnect the iPad, open Settings, and choose "Erase all content". Plug it back into iTunes, update it, and choose "restore backup".