Is there any way to Install Latest Nautilus File Manager in Ubuntu 12.04 LTS

You can try to upgrade several important packages (gtk, glib, etc.) from the ricotz/testing ppa, then compile Nautilus 3.6 from source.

NOTE: Due to you are going to upgrade several important packages of your system, I strongly recommend to do this in a Virtual Machine or in a Test Machine only for testing purposes to see is everything is OK.

Make sure you have enable the "Source code repository"

In the Menu Bar choose Edit -> Software Sources. Click to enable "Source code repository". Just in case I use the "Main Server" to Download.

Then..

• sudo apt-get update

1) Open a Terminal and install the following packages.

• sudo apt-get install build-essential libtracker-sparql-0.14-dev wget

2) Install build dependencies.

• sudo apt-get build-dep nautilus

3) Add ricotz ppa and upgrade the system.

• sudo add-apt-repository ppa:ricotz/testing

• sudo apt-get update && sudo apt-get upgrade

• sudo apt-get dist-upgrade

4) Trash-Full icon in nautilus-places.

Nautilus 3.6.3 use the following icon for the trash-full (user-trash-full-symbolic.svg), not present by default in Ubuntu 12.04.
You can grab the icon from Ubuntu 13.04 to put it in /usr/share/icons/gnome/scalable/status/ directory.

To avoid this:

Once you have the correct icon type in the Terminal.

• sudo mv /path/to/trash/image/user-trash-full-symbolic.svg /usr/share/icons/gnome/scalable/status/
• sudo chmod 644 /usr/share/icons/gnome/scalable/status/user-trash-full-symbolic.svg
• sudo gtk-update-icon-cache /usr/share/icons/gnome/

To look like this:

5) Create a folder to download the source code.

• mkdir ~/Downloads/src

• cd ~/Downloads/src

6) Download the nautilus 3.6.3 (raring) source code from Launchpad.

• wget https://launchpad.net/ubuntu/raring/+source/nautilus/1:3.6.3-0ubuntu16/+files/nautilus_3.6.3.orig.tar.xz

7) Extract the source code.

• tar -xvf nautilus_3.6.3.orig.tar.xz

8) Basic steps to compile & install. (You can change the steps according to your needs, add prefix etc.).

• cd nautilus-3.6.3/

• ./configure

• make

• sudo make install

9) Kill nautilus.

• pkill nautilus

10) Just in case... set default prefereces like show-desktop-icons, no show trash-icon in desktop, etc.

• gsettings set org.gnome.nautilus.desktop trash-icon-visible false

• gsettings set org.gnome.nautilus.desktop home-icon-visible false

• gsettings set org.gnome.desktop.background show-desktop-icons true

11) Finally reboot the system to see the changes.

Result:

Hope this helps.