Shelly has a green and . . . . . . . . black trousers.

Since there is only one pair of trousers which has both green and black colour in it and the indefinite article 'a' has already been used before green no article should be put before black. If we put article before black, then it would change the meaning of the sentence and it will indicate that Shelly has two trousers one is green and one is black.