In in common with many others who have reported, I received "Windows Essentials couldn't be installed" and "Error: 0x800c006" on three NEW Windows 10 Laptops, while in the past I had successfully installed Movie Maker on three laptops with OLDER VERSIONS of Windows 10. I got lucky and thought my good luck might be shared with a few others.

I found quite by accident that following the failed installations the normal Movie Maker loading file had in practice been installed in "C:\Program Files (x86)\Windows Live\Photogallery\MovieMaker.exe" even though every installation reported it could not be installed.  I double clicked "MovieMaker.exe" then agreed to the Licence and the program appears to work normally. I have only tried Movie Maker in a limited way and would be interested if the other programs in Windows Essentials 2012 also installed. Good Luck.