Yes, that's right! However, the alif of the second "al-" is silent, since it is preceded by a vowel - so the phrase would be pronounced as "al-karaju l-kabir".
If we use al before both the word, wouldn't it mean "the garage the big". I know it doesn't make any sense but I'm not really clear. What does al really mean. If it means" the " then the sentence should be "the garage the big". Is there any grammatical solution to this?