Summary: .NET Framework 4 failed to install because of error code HRESULT: 0xc8000222.
Related installation help: Troubleshooting Rhino 5 Installation

Cause:
Some files corrupted in the Software Distribution folder.

Solution:

1. Download Fix_0xc8000222.zip.
2. Extract the Fix_0xc8000222.bat in the zip file to a folder.
3. Right-click on the Fix_0xc8000222.bat and select Run as Administrator.
   
   What this batch file does:
   1) Disables Windows Update Service.
   2) Deletes the C:\Windows\SoftwareDistribution folder which was locked by Windows Update service.
   3) Restarts Windows Update Service.