What is the largest number of courses that one instructor teaches? First count per instructor, then take the maximum of the counts. One query cannot do both:

SELECT MAX(COUNT(*)) FROM teaches GROUP BY id;
ERROR: aggregate function calls cannot be nested

Put the first step in FROM:

SELECT MAX(n)
FROM (
  SELECT id, COUNT(*) AS n
  FROM teaches
  GROUP BY id
) AS per_instructor;

• A subquery in FROM is a derived table. The outer query reads its result like a table.
• Give it an alias (AS per_instructor). Use the alias before its columns, as with any table.
• Name each computed column (COUNT(*) AS n). The outer query needs a name to use it.
• A derived table can be joined to other tables, filtered with WHERE and grouped again.