I believe the fist and the last images you have are for the fibre optic internet connection that EVZ provides.
The way I look at it you have 2 options:
Option1) You can probably run a coax cable from the TV connection (image3) to the room where the TV is in by following the green network cable back from the room (image1) into the connecting box (image3) and then just connecting the new coax cable to the white coax cable box (image2). Cheapest option.
Option2) get one of those coax to cat(network) converters (see image below) and connect one from coax box (image1) to the cat green cable (image3) for the room. and also connect the other side in the same way to give you a coax end from cat connection. Easiest option.
It depends on how capable you are with doing those things and if you have a hook&snake cable lead to follow the cable from one place to another.
Alternatively if you are not able, then get an electrician and have him do the work for you. Will not be cheap though and if you are renting then you will need to get the permission of the landlord.
coax to cat/network, cat/network to coax converter
p.s. sorry if this is too technical, I hope you can understand what I am trying to say.