It is wrong because it is grammatically incorrect in English. In general, you can say "I like blue" or "I like the colo(u)r blue." And in certain contexts, you might also say,"I like the blue colo(u)r." But you cannot say "I like blue colo(u)r."
But if it is incorrect, I am not the right person to argue with, I had to learn this myself.
They said that context means. But in this exersize we don't know context, so both orders may be correct.
While "I like the color blue" is best, it is true that "I like the blue color" can also be used in certain contexts in English. The remaining question is whether the Czech sentence can be translated as "I like THE blue color," in the absence of a demonstrative pronoun. That is something that one of the CZ natives on the team would have to address.
I think it would be "tu modrou barvu".
Out of those colours I like the blue one.
We have no report from you in the system though, so we cannot do anything. If you don't use the "my answer should be accepted" report function, don't expect any action from us no matter what you say in the discussion.
For a question "Jakou barvu máš rád" (What color do you like?) you can answer "Mám rád modrou." (I like blue.).
Please read the discussion above including the link sent by VladaFu.
Then you need an article. "I like the blue paint." It is quite strange here, even when actually painting something with a paiint one would be understood as speaking about a colour when saying "modrou barvu".
"I like the blue paint." would normally be "Líbi se mi ta modrá barva."