On the left if your modem, either cable or DSL. Yellow cable plugs into the router, which then connects to all your devices trying to get internet access. (laptop, phones, TV, etc.) What about this did you "need to know"?
So on the left of that pic is your arris modem. The power cable is the bottom one. The pic that you linked shows the type of cable you'd use on a cable modem. Which would be the top cable. That's the internet as a grey globe.
I'm still not seeing a question. Are you trying to set something up, or just wondering how something works?
Edit: Here is the wiki for the cable/plug that you linked by photo. Perhaps it can help you.
I have an arris modem connected by cable and another cable black like this https://http2.mlstatic.com/9m-negro-wifi-router-wan-wi-...
apart from power cable
and the one on the right I have a netgear wndr3800
What I want to know is what kind of connection I have because I want to apply tweaks for my internet and I need to know the connection if it is adsl, lan or cable just that
Assuming you do have that "F type" plug going into your modem, you have cable, not aDSL. I don't mean to be rude, but if you don't know something this basic, you shouldn't attempt to apply "tweaks". We are at a time now when tweaks aren't really needed.
That looks like a COAX cable, but not exactly. It could be a different connector in other regions. DSL modems plug into phone lines. Cable modems plug in where you normally see a TV or Cable box plugged in. Fiber connections tend to be LAN/Ethernet direct to your router. The fiber comes in as either cable or an optical fiber direct.
I'm not aware of anything you can do to tweak your internet connection. That is up to the ISP and the bandwidth you are paying for. If you want more speed, you have to pay.
Maybe optimizing the traffic will gain you a little bit, but that would just be prioritizing one type of data over another. I can't see how knowing which connection type you have would make a difference.
Good eye Eximo. I missed that. I just saw the threads and stopped looking. After looking at it again I thought it might be a normal F type plug with a female to female adapter on it, used to connect two cables together. But it's not that either because of the center wire. I don't know what plug that is.