Installing Linux Kernel 4.x on Debian 8

Add the debian / jessie-backports into /etc/apt/sources.list

echo "deb http://ftp.us.debian.org/debian/ jessie-backports main" >> /etc/apt/sources.list
echo "deb-src http://ftp.us.debian.org/debian/ jessie-backports main" >> /etc/apt/sources.list

Run apt-get update,

apt-get update 

You can now install the 4.x kernel,

apt-get install -t jessie-backports linux-image linux-image-amd64

You'll now need to reboot the VM/Server to boot into the new kernel

reboot

You can verify that the 4.xx kernel is installed by running the command "uname -r" and you should see similar output,

root@localhost:~# uname -r
4.9.0-0.bpo.2-amd64

Done!