Take a look at this announcement post:
Officially as a flavour, 16.04 is no longer supported... but many regular Ubuntu packages will still receive updates until April 2021.
You can run this command in the Terminal to find out what's supported on your system:
ubuntu-support-status
Historically, there was an upgrade for MATE Desktop from 1.12 to 1.16 by adding this PPA:
sudo add-apt-repository ppa:ubuntu-mate-dev/xenial-mate
sudo apt update
sudo apt dist-upgrade
The last decimal of the release is like a 'snapshot' indicator, so installing 16.04.6 would provide all the latest packages from the ISO up to that release date, which is also the same as taking 16.04.2 and applying all updates, which will update everything to 16.04.6.
As far as I know, .6 is the last point release of an Ubuntu cycle.