Now that I've seen what you're looking at, let me show you a few things from my collection of links to well-designed coops.
Remember your sizes -- for 4 chickens you need:
I strongly recommend a full-height attached run instead of a half-high one. The short run is a killer on your back and last summer I ended up with a bunch of staples in my scalp after hitting my head on a hook inside my brooder.
https://www.backyardchickens.com/articles/dallas-urban-coop-single-slope-design.72422/ This is similar to the one you linked, but with a better roof slope and upper-level ventilation. Those vents and windows would benefit from top-hinged covers in a wetter climate than Dallas.
https://www.backyardchickens.com/articles/yakisugi-coop.76398/ One of the most thoughtfully-designed coops on this website, perhaps anywhere. It's probably not what you want, but it's a good read to show how to make design decisions and has extraordinarily-good ventilation for such a small coop.
https://www.backyardchickens.com/articles/coreys-coop-de-doop.55619/ Another coop-and-run combo. Again, the venting would benefit from top-hinged covers to keep weather out in season.
Remember your sizes -- for 4 chickens you need:
- 16 square feet in the coop. 4'x4' is the only really practical build for this given the common dimensions of lumber.
- 4 feet of roost
- 40 square feet in the run. 4'x10' or 5'x8'. 6'x6' is a bit too small, 6'x8' is more generous and easier to build than 5'x8'.
- 4 square feet of ventilation. A 2'x2' window is theoretically enough, but in practice doesn't create any air FLOW so better to spread the venting around (and even better to exceed the minimums, especially in warm climates).
- 2 nest boxes, to give the hens a choice
I strongly recommend a full-height attached run instead of a half-high one. The short run is a killer on your back and last summer I ended up with a bunch of staples in my scalp after hitting my head on a hook inside my brooder.
https://www.backyardchickens.com/articles/dallas-urban-coop-single-slope-design.72422/ This is similar to the one you linked, but with a better roof slope and upper-level ventilation. Those vents and windows would benefit from top-hinged covers in a wetter climate than Dallas.

https://www.backyardchickens.com/articles/yakisugi-coop.76398/ One of the most thoughtfully-designed coops on this website, perhaps anywhere. It's probably not what you want, but it's a good read to show how to make design decisions and has extraordinarily-good ventilation for such a small coop.
https://www.backyardchickens.com/articles/coreys-coop-de-doop.55619/ Another coop-and-run combo. Again, the venting would benefit from top-hinged covers to keep weather out in season.