Find the number of employees working under a manager

Since each branch can only have one manager, you can count the number of employees in a branch and then join the manager to their branch. From there you can count the number of employees in each branch.

SELECT manager.id               AS manager_id,
       manager_employee.name    AS manager_name,
       COUNT(employee.id) - 1   AS employee_count
  FROM manager
 INNER JOIN employee AS manager_employee
    ON manager.employee_id = manager_employee.id
 INNER JOIN branch
    ON manager_employee.branch_id = branch.id
 INNER JOIN employee
    ON branch.id = employee.branch_id
 GROUP BY manager.id,
          manager_employee.name