Anybody here able to help me with this question regarding relativity?

I have been doing some reading trying to at least make some sense of the special theory of relativity, which is said to be much easier to understand than the general theory.

Here is my question. Suppose I have two flashlights, one pointing left and the other pointing right. I flash a signal from the two of them at the same time. After a second goes by, one light signal will be 300,000 km to my left and the other will be 300,000 km to my right, so the distance between them is 600,000 km, meaning that they are traveling twice the speed of light relative to one another. What have I got wrong?