According to https://support.microsoft.com/en-us/kb/2734782, there are 4 resolutions for getting a 0x800F0906 error when trying to turn on .NET 3.5 in Programs and Features. Unfortunately, the first two involve blaming someone else, and the last one is for Windows Server 2012 and 2012 R2. Fortunately, the 3rd alternative works for fixing your Windows 8.1/10 .NET 3.5 installation error 0x800F0906:

  1. Find Windows media and insert it into a DVD (or whatever) drive. I will assume the drive is D: in the instructions below, so substitute the correct drive letter if it is not.
  2. Open an elevated command prompt by finding Command Prompt, right clicking on it, and choosing “Run as administrator” from the menu.
  3. Type: dism /online /enable-feature /featurename:NetFx3 /All /Source:D:\sources\sxs /LimitAccess

Be sure to reboot afterwards so it takes effect.