Windows 10 has DirectX out of the box. That is, you need not do anything at all ever unless your Windows installation is broken. The OS will be given all of DirectX by itself without any user decisions as allowed for that version of the OS.
If you're having problems with your Windows installation (which you likely will be if DirectX is broken or are having update failures with an update like this) then I'd suggest doing an in-place upgrade or clean installing the OS. Both of those will fix the Windows installation including DirectX and both start here: https://www.microsoft.com/en-us/software-download/windows10
The rest of dx12 issues will be GPU and GPU driver related. Also the game if you want to add that in there.
That is all there is to it. Because you're having update problems and problems with DirectX then its not a great idea to try poking at little things here.
To answer your question directly:
"DirectX versions and updates by Operating System...
*Windows 10...*
DirectX 11.3 and 12 are included with these Windows versions.
*Updates will be available through Windows Update. There is no stand-alone package for these versions of DirectX."*
Hope the best :)