But if it is incorrect, I am not the right person to argue with, I had to learn this myself.
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.
The Czech sentence uses the accusative singular, modrou barvu. While "I like blue colors" is a valid English sentence, It is not a translation of the exercise sentence, because it changes the object from singular to plural, for which there is no need or justification. "I like the color blue" would be an alternative to the translation shown above, if that works better for you. Please feel free to answer VladaFu's question, if you like.
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."