Virtualbox: cannot create new VMs nor add existing VMs

This is why I mentioned

If kernel headers - for your active kernel - is not present - dkms will fail - it depends on the correct headers - again - the default choice is never or rarely correct.

Add the headers for your active kernel - using your information

sudo pacman -Syu linux612-headers

[root tip] [How To] Kernel - Headers - DKMS