I may have answered my question, although there maybe a better way:
select manager_name, business_brand from manager, business, manager_business where manager.manager_id = manager_business.manager_id and manager_business.business_id = business.business_id and manager_name like '%john smith%'
ON manager_business.manager_id = manager.manager_id
ON business.business_id = manager_business.business_id
WHERE manager.manager_name LIKE '%john smith%'