"Can you give an example of a genetic mutation or evolutionary process that increases the information contained in the genome?"
According to Richard Dawkins... well, he didn't give an answer. Well, we are provided with a clip of him later on explaining that evolutionary theory does not espouse that humans or apes evolved from each other but rather a common ancestor, but that doesn't really answer the question, and anyone with a hand in this discussion should be familiar with the theory. Anyone who was forced to attend the secular indoctrination known as public schooling should know that.
Crush a fool in a mortar and pestle with grain, and he will not depart from his foolishness.