What is it with all the ask threads?
If you are running a simple cable, or indeed even a local network, you should not need port forwarding unless you are running a super secure setup that wants you to individually OK network activity or some truly bizarre setups with a firewall. As it sounded like you were using standard normal user Linux mint (no SElinux addons or server type setups) this should not be the case.
Static IP you will want for both machines unless you run a DHCP server on one of them. You can skip this by going into any place that sells electrical junk (you might even have one in a box), buying an old router and using that. You don't need it to go on the internet, you don't need it to have super fast wifi, you don't need gigabit ethernet for 2 player minecraft as the 100mbps of a basic router is still likely faster than your internet out into the world, you don't need any of the fancy options -- as long as you can plug the cable in and have a LAN (don't think I have ever seen consumer stuff block LAN like they might for guest wifi) it should solve a lot of woes here.
Static IP is a fairly common thing to be doing on networks so every OS should have something. You might have to go into the advanced network settings somewhere to find it though. For the sake of being both obvious and skipping some of the more technical details you will likely have between 3 and 5 things to fill in
1) IP address
2) Subnet mask
3) Gateway address
4) Primary DNS
5) Secondary DNS
IP address is fairly basic. Personally for you I would say just use one of the 192.168.1.??? options where ??? is between 1 and 254.
I will skip the subnet mask reasons, calculations and everything else. It should autofill with 255.255.255.0 for the 192.... stuff above but if you have to then put that in.
Gateway does not matter. In normal cases it is where your router is so you can access the outside world. If you don't need outside internet (or are not on one) then who cares.
DNS does not matter if you don't have internet. It is what converts nice text based website addresses into IP addresses of the servers. Your ISP will typically provide you with one but many choose to use either google's or something like opendns https://www.opendns.com/
You might not even have this. Everything else is optional. Ignore anything about IPv6 as you want IPv4 right now.
Remember to put it all back to automatic once you want to plug back into a normal network. If you want to do this computer thing I would suggest learning about what each of those do and how they work, and probably for ipv6 as well (we are sort of technically maybe in the middle of transitioning between IPv4 and IPv6 in the world right now, though IPv4 will probably continue to be primary use example for another decade or so at this rate).
I have set up minecraft servers for people (a restaurant wanted one for an evening they did once, and I duplicated it for someone else). The server stuff was basic enough (you download the server, set up the options and run it) and there are a billion guides to that one if you somehow need one. I will note however that by default the server will have an option to want to look up player skins (and by extension ensure they are not sharing or pirating) online. You can disable this easily enough. It got unofficially known as pirate mode but if you are doing truly offline versions then you will want that.
I am less familiar with direct LAN connections outside of the portable versions. In theory it should just be a matter of one player hosting a game, the second player going to network game, typing in the host address (if you set up a static IP before then that, if you are using a router go look it up on the router or grab it from the other machine) and pressing join.
Theoretically you could host a server and play it on the same machine (and have the other join) but I am less familiar with what might need to happen there, not to mention we might need to actually do something fun with localhost instead.