The book refers to the Hebrew calendar as evidence that the moon has not moved for the past 6,000 years or so. This is because the Hebrew calendar is one based on the phases of the moon.
Unfortunatly, the Hebrew calendar now running strong in the year 5,763 has only existed for about 3,000 years. At this time, the high priests of Solomon's Temple created the calendar which had a begining date to coincide with the begining of the world. They looked at the stories in the Torah, and decided with all the characters in the Torah leading up to that point and adding up all their ages, the world was created some 3,000 years prior. While this means that a literal interpretation suggests that the world is only 5,763 years old, niether I nor any other Jew I've met have ever suggested the world was anything less than several billion years old. Regardless, people have kept close tabs on the calendar since its creation some 3,000 years ago. So, you could say that according to the Hebrew calendar the moon has moved only a negligible amount in the last 3,000 years, but not 6,000 unless you want to use an unreliable source(the bible) as evidence of such.