The full installer for Mac OS X Mountain Lion is still available for purchase from the Apple Online Store
(not the App Store) for $20, if you purchase Apple will send you an e-mail with a redemption code.
But there is absolutely no need for you to purchase Mountain Lion if you want to upgrade to macOS High Sierra.
You can download and install Mac OS X El Capitan 10.11.6 for free, then upgrade to macOS High Sierra 10.13.6 for free.
Open Safari and click on this link,
How to get old versions of macOS – Apple Support
Go to Download OS and click on OS X El Capitan 10.11
this downloads InstallMacOSX.dmg to your Downloads folder.
The next section can only be done on a mac that is capable of running El Capitan.
This includes macs that have the potential to run El Capitan but have been upgraded to a newer OS.
A mac that came preinstalled with an OS later than El Capitan will refuse to do the next bit.
When downloaded open to InstallMacOSX.pkg, double-click on
that and an installation window will open, this does not install El Capitan
but converts the InstallMacOSX.pkg to the Install OS X El Capitan.app which
you will find in your Applications folder, it should be 6.2GBs in size.
(If the installation window asks which disk you want to install to, you must pick
the disk that you are booted to at the time. Not any internal or external disk that
you want to eventually install El Capitan on, that is for later.)
To start the installation of El Capitan double click on the Install OS X El Capitan.app.
The copy of the install app self deletes after installing El Capitan, so make sure you keep a copy of the
InstallMacOSX.dmg if you need it in future, or you could just make a copy of the Install OS X El Capitan.app
prior to installing and moving it to an external drive for safe keeping.
It is also possible to create a bootable USB installer disk using the Install OS X El Capitan.app in the Applications
folder and the createinstallmedia command in the Terminal app.
Read the instructions here,
How to create a bootable installer for macOS – Apple Support
After installing Mac OS X El Capitan you can then download and install macOS High Sierra,
Open Safari and click on this link,
How to get old versions of macOS – Apple Support
Go to the Download OS section and click on macOS High Sierra.
Before upgrading make a full back up of your Mac.
Check that third party apps you use have updates available for the new OS.
https://roaringapps.com
Check that your printers/ scanners etc have updated drivers and software available for the new OS.
Connect your mac to your router via cable rather than rely on WiFi.
Do not use your mac while it is downloading
and do not use any other devices that share the same internet connection.
If the App Store says ‘Open’ then it is detecting a previous download of the install app
go to the Applications folder locate Install macOS High Sierra.app.
Move it to the Trash, empty the Trash.
Restart, click on the link again, the App Store should say ‘Get' or 'Download'.