Here is a very easy way to update kernel for LinuxMint 64 bit. I found the instruction here: https://mintguide.org/system/639-install-linux-kernel-4-7-stable-on-linux-mint.html
Basically what I did was following:

1. Download linux-image and linux-headers:

$ mkdir temp
$ cd temp
$ wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.8.8/linux-headers-4.8.8-040808_4.8.8-040808.201611150231_all.deb
$ wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.8.8/linux-headers-4.8.8-040808-generic_4.8.8-040808.201611150231_amd64.deb
$ wget http://kernel.ubuntu.com/~kernel-ppa/mainline/v4.8.8/linux-image-4.8.8-040808-generic_4.8.8-040808.201611150231_amd64.deb

2. Install all .deb files:

$ sudo dpkg -i *.deb

3. Update GRUB:

$ sudo update-grub

4. Reboot:

$ sudo reboot

5. Check the kernel version:

$ uname -r

That’s it!