В терминале:

$ inxi -S
System: Host: note Kernel: 4.15.0-54-generic i686 bits: 32
        Desktop: MATE 1.20.1 Distro: Linux Mint 19 Tara

или

$ cat /etc/lsb-release 
DISTRIB_ID=LinuxMint
DISTRIB_RELEASE=19
DISTRIB_CODENAME=tara
DISTRIB_DESCRIPTION="Linux Mint 19 Tara"

или

$ cat /etc/issue
Linux Mint 19 Tara \n \l