All of this is just going off checking Wikipedia, so it could be wrong. Gluons are a type of particle that can have nine different "color states" depending on the quarks and anti-quarks that comprise them (despite the name, it has nothing to do with literal color). These states are made up of red, green, and blue for quarks, and anti-red, anti-green, and anti-blue for anti-quarks. Depending on the combinations of quarks and anti-quarks, the color state of gluons listed something like "red-antigreen" as "rg", with the "g" having a line over it to show it's anti-green, not green. Since you can have a color matched with the anti-version of its color, like I said earlier, you get 9 potential color states.

Then, of those 9 color states, you have combinations of two gluons of different types of states that combine. If you have a strong, stable version of this state, it's called a color state singlet. Particles like protons have this state, and it allows them to interact with other particles that also have color singlets. However, gluons can't interact at long range, that means they also can't hold a color singlet.

So, that leaves 8 potential color state couplets that can be formed. I have no idea why there's only 8 valid arrangements of those 9 couplets that aren't a stable singlet, but apparently you can only get 8.

Also tagging @Owl@mander.xyz because I don't think they'd get notified.

Edit: Sorry for the reply after it got answered. There was nothing when I started and it just took a while to figure it out.