For purposes of discussion, the following response to the posted question -- how did William Shakespeare use the motif of darkness in his play Romeo and Juliet -- assumes that the question is multiple choice. If the student's intent is otherwise, then perhaps he or she can repost the question in a clearer manner.
Darkness has served to emphasize underlying themes in the arts for thousands of years. It can suggest foreboding, depression, terror, and any other negative emotion the author/painter/film director hopes to emphasize. In general, lightness equals enlightenment, joy, and optimism; darkness equals the opposite. In the case of Shakespeare's play, the use of darkness highlights the emotional transformations that affect the titular characters throughout. That Shakespeare adroitly used the contrast of light and darkness to emphasize emotions and establish tone. The negative connotations of darkness are employed in the service of a play intended as a tragedy, evident in the fact that the full title of the play is, in fact, The Tragedy of Romeo and Juliet, not simply Romeo and Juliet.
In Act I, Scene II, Capulet, leader of the clan that bears his name and Juliet's father, discusses his arrangement for his daughter to marry Paris, suggesting in their conversation that such a union will illuminate an otherwise bleak environment: "At my poor house look to behold this night Earth-treading stars that make dark heaven light." Later, in Act III, Scene V, Romeo stands beneath Juliet's balcony. These two young lovers, their fates predetermined by forces beyond their control, lament the predicament in which they exist. As Juliet, fearing discovery, urges Romeo depart before he is spotted, Romeo equates their imminent separation with darkness:
Juliet: O, now, begone. More light and light it grows.
Romeo: More light and light; more dark and dark our woes.
In responding to the student's question, therefore, one must conclude that Shakespeare employed darkness as a means of conveying or emphasizing sorrow and fear, especially the former.