This will also patch the Meltdown/Spectre security bug.
- Kernel 4.4 is supported until 2021
- Kernel 4.13 is supported until 2018 August
- Kernel 4.15 is supported until 2023 April
- All other kernels shown in Update Manager are not supported anymore, they don't receive any (security) updates anymore
Open Update Manager (it's in your mint menu, you can also open it by clicking the grey shield icon on your panel (taskbar))
In Update Manager in the menu bar click View >> Linux Kernels
You'll see something like this:
In the left column, choose whichever kernel version you wish to install (if you were told to upgrade kernel in #linuxmint-help, you'll want to install 4.13 or 4.15, if you don't know which one, ask whoever told you to upgrade)
In the right column, choose the highest number available
Click Install and wait for the installation to complete
In order to activate the new kernel, you'll have to reboot.IMPORTANT NOTICE:
If you do experience problems while booting, hold down left SHIFT key while booting to enter the GRUB menu, here you can choose to boot from your previously working kernel. (letter E for advanced boot options)
It is highly advised to always keep at least 1 kernel that you know was working on top of the kernel you're currently using, so that if you ever run into issues, you can go back to a previous kernel that you knew worked.