"The big garage" would be "اَلْكَراج اَلْكَبير". As you can see, in this case you should add "al-" before the adjective as well.
The meaning is the same a big garage or a garage is big is not a matter of right or wrong it is purely what you want duolingo. Your acceptance protocol should be able to accept these differences and accept the answer!
I've already discussed this at length, your acceptance protocol should be altered to accept an answer stating either the big garage and the garage is big!
While they, as stand alone phrases, are similar in meaning, their usage in sentences is very different, i.e. they can be used interchangeably neither in English nor in Arabic (as otherwise there would not be two different grammatical constructions to begin with). Therefore, the point of this exercise is to translate not only the meaning, but the grammatical construction as a whole. There is no point in mixing those up, especially for the beginners.