A good way to approach this question is to first decide which of the four styles best describes you, and then support your choice with examples.
For example, if your preferred style is supportive, you might write that you tend to listen carefully, cooperate with others, and consider people's feelings before responding. Benefits of this style include building trust, reducing unnecessary conflict, and helping other people feel comfortable expressing their ideas.
However, every communication style can create roadblocks when taken too far. An excessively supportive communicator might avoid necessary disagreements, have difficulty saying "no," or place other people's preferences ahead of his or her own. This can prevent problems from being addressed directly.
A useful style to flex into could be the directive style. Directive communicators tend to be decisive, straightforward, and focused on accomplishing objectives. Developing some of these characteristics could help a supportive communicator become more comfortable stating expectations, making decisions, and addressing disagreements directly.
The important part of your answer is to relate these ideas to your own experiences. Give an example of when your preferred style helped you communicate successfully, an occasion when it created difficulty, and a situation in which adopting another style could make you a more effective communicator.