Decisions of Board of Appeals. The Board of Appeals may reverse or affirm, wholly or partly, or may modify the order, requirement, decision or determination appealed from and may make such order, requirement, decision or determination as ought to be made and to that end shall have all the powers of the Building Inspector. The concurring vote of four members of the Board of Appeals shall be necessary to reverse any order, requirement, decision or determination appealed from, or to decide in favor of the applicant on any matter on which it is required to pass, or to effect any variation in the requirements of this chapter. The grounds of every such determination shall be stated and recorded. No order of the Board of Appeals granting a variance shall be valid for a period longer than six months from the date of such order unless the building permit is obtained within such period and the erection or alteration of a building is started or the use is commenced within such period.