Can a teenager take advil (ibuprofen) for headaches?

Yes: 400 mg or even 600 depending on the size of the teen. Always take it with food. Check with your doctor if there are other medications the patient is taking to be sure there is no drug interaction. See your doctor if the headaches are getting worse, happening more often, or if they are accompanied by other symptoms such as difficulty walking, unsteady gait, vision changes, personality changes etc.