If you're getting an installation error code of 0x800F0906 while trying to install .NET Framework 3.5 on a Windows 8 or Windows Server 2012 system, it's because the initial installation source isn't available and you're most likely using WSUS without an appropriate Group Policy Object to redirect to an alternate installation path.
There are a few ways of handling this - use the installation media and DISM to install it, set up a GPO to use Windows Update as an alternate installation path, or copy the WinSxS folder off the install media to a network share and configuring a GPO to use this share as an alternate installation path.
If you have the installation media and you need to only do this for a single PC, then the following command will work:
dism.exe /online /enable-feature /featurename:NetFX3 /Source:D:\sources\sxs
You may need to replace D: with the drive letter containing the installation media.
To configure a GPO to use Windows Update, open up Group Policy Management, create and edit a new GPO. Go to Computer Configuration, Policies, Administrative Templates, System. Open up "Specify settings for optional component installation and component repair", change the setting from Not Configured to Enabled and tick "Contact Windows Update directly to download repair content instead of Windows Server Update Services (WSUS)". Click OK, close the Group Policy Management Editor window and link the GPO to an appropriate container in AD, then run gpupdate /force on the affected computer.
If you want to configure a GPO to use a network share, copy the \sources\sxs folder from either a Windows 8 or Windows Server 2012 DVD/ISO to an appropriate location on a server (e.g. \\server\install\win8sxs), then create and edit a new GPO as outlined above. Instead of enabling the WSUS option though, put the network path to the SxS folder in the field for "Alternate source file path".
Microsoft also have a knowledge base article on this here - Error codes when you try to install the .NET Framework 3.5 in Windows 8 or in Windows Server 2012