You may have noticed that Parts can't be dragged and dropped on the Organize page the way that chapters can.
This is because Parts serve as containers of the chapters. They aren't individual posts like a chapter, but instead are whole sections of your book that may contain many individual posts.
In order to reorder a Part and its chapters in your book:
1. Hover over the name of the Part on the Organize page and click Edit
2. In the Part Attributes panel, insert the number that you wish the Part to appear in order of the other Parts in the book
3. Click Save
4. Repeat the process for each Part
The Parts should appear in the order you've dictated when you view them on the Organize page.