What does "genus VI" mean in mycology?
This is a multi-part series of books, with each volume numbered with roman numerals I, II, III, IV, etc meaning 1, 2, 3, 4, etc, followed by a subtitle, in this case the subtitle is "Modern Genera."

There is no meaning to "Genus VI", the title of the book series is "How to Identify Mushrooms to Genus" which indicates it will help you identify mushroom genus but will probably not bother with differentiating species of the same genus (even that is quite a lofty goal).

The authors could have instead called this book "How to Identify Mushrooms to Genus; Volume 6: Modern Genera" to convey the same meaning.