Right-click the patch file and "Run as Administrator."
If you own the game on Steam, you do not need a manual download link. Steam automatically applies the 12.2.2 update. To verify your version: Launch Football Manager 2012.
If you have located the standalone .exe for the 12.2.2 patch:
While the heyday of (FM12) was over a decade ago, many veteran managers still consider it the "sweet spot" of the series. It combined the speed of the older engines with the tactical depth that defined the modern era. However, to get the most stable experience, ensuring you are running the final 12.2.2 patch is essential.