Final answer:
The most common way publishers approach authors is through authors using agents to help them find and negotiate with publishers.
Step-by-step explanation:
The most common way publishers approach authors with requests to write books is through authors using agents to help them find and negotiate with publishers. This method involves authors hiring literary agents who have connections within the publishing industry. The agents will then submit the author's work to publishers on their behalf and negotiate contracts and deals if there is interest in publishing the book.