How to join tables when one of them doesn't have any relationship with the others
How about this:

SELECT Authors.manufacturers_id AS AuthorID, Authors.manufacturers_name AS AuthorName, count(products.products_id) AS '# of Products'
FROM Authors
LEFT JOIN
(
    SELECT manufacturers_id,SUBSTRING_INDEX(SUBSTRING_INDEX(t.manufacturers_name, ',', n.n), ',', -1) value
      FROM Manufacturers t CROSS JOIN 
    (
       SELECT a.N + b.N * 10 + 1 n
         FROM 
        (SELECT 0 AS N UNION ALL SELECT 1 UNION ALL SELECT 2 UNION ALL SELECT 3 UNION ALL SELECT 4 UNION ALL SELECT 5 UNION ALL SELECT 6 UNION ALL SELECT 7 UNION ALL SELECT 8 UNION ALL SELECT 9) a
       ,(SELECT 0 AS N UNION ALL SELECT 1 UNION ALL SELECT 2 UNION ALL SELECT 3 UNION ALL SELECT 4 UNION ALL SELECT 5 UNION ALL SELECT 6 UNION ALL SELECT 7 UNION ALL SELECT 8 UNION ALL SELECT 9) b
        ORDER BY n
    ) n
     WHERE n.n &lt;= 1 + (LENGTH(t.manufacturers_name) - LENGTH(REPLACE(t.manufacturers_name, ',', '')))
     ORDER BY value
) AS manufacturers ON manufacturers.value = Authors.manufacturers_name
LEFT JOIN products ON manufacturers.manufacturers_id = products.manufacturers_id
GROUP BY Authors.manufacturers_id, Authors.manufacturers_name