How did the Enlightenment help bring about the Declaration of Independence?
You could answer this in two ways.
First, the Enlightenment helped to bring about the American Revolution in general. The idea of democracy and that there was no rational basis for monarchy was a major Enlightenment idea. Since the Enlightenment helped lead to the Revolution, then it also helped lead to the Declaration.
Second, the ideas of Enlightenment thinker John Locke are echoed in the Declaration. Locke was the one who said that governments get their power from the consent of the governed. He was the one who said that people have natural rights, among them the right to life, liberty, and property. So his ideas were reproduced by Jefferson in the Declaration.
In these two ways, the Enlightenment helped bring about the Declaration of Independence.