A zoning board of appeals appointed pursuant to section 14-408 shall hear and decide appeals from and review any order, requirement, decision, or determination made by an administrative official charged with the enforcement of any ordinance adopted pursuant to sections 14-401 to 14-418. The zoning board of appeals shall also hear and decide all matters referred to it or upon which it is required to pass under any such ordinance. The concurring vote of four members of the zoning board of appeals shall be necessary to reverse any order, requirement, decision, or determination of any such administrative official, or to decide in favor of the applicant any matter upon which it is required to pass under any such ordinance or to affect any variation in such ordinance.