No error in output, but yet the color doesn't change as its support to?

Well, you didn't provide too much info but I think I see the issue. You're doing:

game.StarterGui.KeemTroll2.Main.cmds.BackgroundColor3 = Color3.new (24, 255, 62)

That won't work because a Color3.new() value ranges from 0 to 1. Here's your issue solved:

game.StarterGui.KeemTroll2.Main.cmds.BackgroundColor3 = Color3.fromRGB (24, 255, 62)

Hope I helped! :)

Astreal is correct, but you have another problem. You're making your changes to the gui in StarterGui.

StarterGui isn't actually what the player is seeing, it is merely a container to store guis, which later get cloned into the PlayerGui. The gui in the PlayerGui is what your players are seeing. They won't see any changes made to the objects in StarterGui until they respawn.

So basically, make your changes to the guis in the PlayerGui. It's hard to give code because I don't know your hierarchy, but it'll be something like this:

script.Parent.MouseButton1Click:connect(function()
    script.Parent.Parent.cmds.BackgroundColor3 = Color3.fromRGB(24, 255, 62)
end)