Although it's been some time since the OP asked the question, this is still relevant as I've faced the same situation recently after finishing experimenting with the Gnome3 PPA on my 16.04 system. Updating with this PPA resulted in Nautilus and a few other packages being upgraded (the OP's screenshot shows Nautilus 3.18, which is what I was upgraded to).
In my case, I checked my /var/log/dpkg.log (grep for "status installed" to make scanning easier) to identify the packages I had upgraded from the PPA. These were:
Your particular case may vary, but for the purposes of restoring Nautilus the first three packages were the ones I needed to downgrade.
After removing the Gnome3 PPA, I used apt-cache policy to verify for each of the three nautilus packages the installed version and the repository version (the one I wanted to downgrade back to), e.g.:
$ apt-cache policy libnautilus-extension1a
*** 1:3.18.5-0ubuntu1~xenial1 100
500 http://gb.archive.ubuntu.com/ubuntu xenial-updates/main amd64 Packages
500 http://gb.archive.ubuntu.com/ubuntu xenial/main amd64 Packages
For my 16.04 system, I needed to downgrade from the PPA's "1:3.18.5-0ubuntu1~xenial1" back down to "1:3.18.4.is.3.14.3-0ubuntu5".
For anyone still on 15.10, the applicable version is "1:3.14.2-0ubuntu13".
Apt allows you to downgrade packages to specific versions, by following the package name with an equals sign (see man apt for details). apt install --reinstall didn't work for the OP as that is not the correct syntax to tell apt to downgrade. In my case, I was able to successfully downgrade Nautilus using:
sudo apt install libnautilus-extension1a=1:3.18.4.is.3.14.3-0ubuntu5 nautilus-data=1:3.18.4.is.3.14.3-0ubuntu5 nautilus=1:3.18.4.is.3.14.3-0ubuntu5
If you don't do all three packages, you'll have problems such as nautilus not starting, as the 3.18 Gsettings schema lacks some keys that are in the 3.14 schema. Gsettings/dconf is where critical configuration is kept for Nautilus and various other apps;
~/.config/nautilus has some settings, but not all.