"Knowing that" has only to do with the fact that a person knows "what" happens or has happened. "Knowing how" implies that the person understands the mechanism that makes something happen.
For example, I know that the internet works and I know that computers work. However, I do not really know how either of those work. I cannot really explain to you how my typing is made into letters on this page or how the page is made or how the information I type is transmitted to the computer where this site is.