"J'aime une couleur, le vert."
The translation of "J'aime une couleur, le vert." is : "I like a color, green" or "I like one color, green" depending of the context.
Please note that in this exercise "vert" is a noun.
"J'aime la couleur verte" would be "I like the green color".
In this case "vert" would be an adjective, so you need to match it with the noun. Here "couleur" is feminine so "vert" will change for "verte".
Doesn't this really say "I like one color, green"? Would "J'aime la couleur vert" make more sense as a translation for "I like the color green"?
Why is it vert (masculine) and not verte (feminine) because of La couleur? ...Well, probably because it's not the green color but just green without describing the color?
'la couleur rouge' translates to 'the colour red' (see duolingo Basics Lesson examples for this word). The use of the word 'rouge', in that example, as a noun, does not necessitate modification of sentence structure. If that example is not a mistake, then 'j'aime la couleur rouge' should be acceptable here.
Except that it's "J'aime une couleur, le vert" = "I like the colour green." in this exercise. The words "red" or "rouge" don't have their place here.