An installation of Skype in version 8.xx is a little bit different than it was with Skype 4.xx from what I found. As of writing this the current version of Skype is 8.11 and the procedure that I’ve checked on 2 computers was:
- Download DEB package with Skype from https://www.skype.com
- Check if GDebi is installed in your system. If not, install it from a repository. I used Synaptic package manager for this.
- Open downloaded DEB file (skypeforlinux-64.deb) with GDebi. To to this right-click on the file. On Linux Mint with Mate the context menu already contained “Open with GDebi” as the first menu-item. On Linux Ubuntu with Cinnamon one has to select “Open with…” menu-item and then select GDebi from the sub-menu.
- Click on “Install” button and provide your password
Done!
This worked for me under Linux Mint 17.3 and Linux Ubuntu 16.04 both being 64-bit.
Afterword
Please note that Skype is not an open-source software and I don’t recommend it. This article is just providing an instruction how to get latest Skype version working on Linux in case you need it.
If you know the open-source alternative to Skype that is available on Linux and allows video-calls and it quite stable and somehow popular then please let me know.
The Art of Code 
why do you use linux mint? better in any way than ubuntu?
Linux Mint is a close relative of Linux Ubuntu however it has some nice (for me) features out of the box. For instance: my favourite desktops (Mate/Cinnamon). Another reason is a colour theme that I find to be hard to change easy. Ubuntu is so brown-and-orange! On the other hand Mint is so grey-and-green what I prefer 🙂