Adding Cat6 Surface Mount Box
Wrong Jack
That is NOT a normal CAT6 (or even CAT5, or to be honest, not even CAT3) jack. That is an &quot;old style&quot; phone jack, just happens to have 8 pins.
I can't tell easily whether you have the wires matched up correctly. If they're not matched correctly then it is guaranteed to not work. However, CAT6 (and CAT5 and even CAT3) normally:

Use colored pairs (Blue, Orange, Green, Brown) in T568A or T586B configuration. Even if the actual wires are not in those colors, the jack will have markings to indicate how to match your cable wires to the jack.

Use a punch block rather than screw terminals. This allows for very consistent and reliable termination using a punch tool.

Use twisted pairs except for the very end. In this case you have separate wires from each screw, not twisted pairs, which is I think a key reason for a punch block instead of screw terminals.


What you need is a CAT6 jack such as:
https://www.homedepot.com/p/Commercial-Electric-Category-6-Jack-White-5016-WH/206428120
and a surface mount box to install it in, such as:
https://www.homedepot.com/p/Commercial-Electric-2-Port-Category-5e-and-Category-6-Surface-Mounting-Box-5322-WH/206428219
and a punch tool such as:
https://www.homedepot.com/p/Commercial-Electric-Impact-Punch-Down-Tool-with-110-Blade-CE70804/202039354
Actually that particular jack includes a (effectively, as it will likely break) single-use punch tool. But if you have more than 2 jacks to install, get a punch tool. The same punch tool (make sure it is 110 type, not 66) will work for CAT 3, 5, 5e, 6.
The brand of the parts does not matter much. Leviton is a big name brand, but I've used plenty of others as well. What does matter is that the jacks &amp; the surface mount boxes (or wall plates, which mount on a standard electrical box or box eliminator) are compatible - there are some variants with slightly different sizes. Cat 3, 5, 5e, 6 all work pretty much the same. However, using an older type will not necessarily get you full error-free operation at the higher speeds of the newer types due to differences in twists and other factors. In other words, if you use CAT 3 jacks with CAT 5e or 6 cable, you may find that you can't get Gigabit speeds even though simple testers will show a good electrical connection.
Most good CAT 5/5e/6 jacks (even from &quot;off brands&quot;) will show color-coding for both T568A and T586B. It doesn't matter which one you use, as long as you use the same on both ends of the cable.