I am on elementary os loki 0.4 can I downgrade to linux kernel 3(any 3 version) or does Loki just supports 4. thank you.
You can easily downgrade ( or upgrade ) to any kernel ( even 4.11 ). You could use the CLI to do so. Or you could get Ukuu Kernel Updater.
To install Ukuu type into terminal :
sudo apt-add-repository -y ppa:teejee2008/ppa
sudo apt-get update
sudo apt-get install ukuu
However after downgrading do not remove your stock kernel. If in case anything goes wrong you could revert back to your old kernel. ( And BTW why would you want to "downgrade" the kernel ? ) .
Elementary OS Loki build on Ubuntu 16.04.2 LTS. Ubuntu 16.04 LTS is based on the long-term supported Linux release series 4.4 kernel. I don't think you can do it. If you can do it, you may encounter too many errors.