Unless such proposed amendment, supplement, or change has been approved by the zoning commission or if a protest against such proposed amendment, supplement or change has been filed with the city clerk duly signed and acknowledged by the owners of twenty percent (20%) or more either of the area of the lots included in such proposed change or those immediately adjacent on the rear thereof extending two hundred feet (200') therefrom or of those directly opposite thereto extending two hundred feet (200') from the street frontage of such opposite lots, such amendment shall not become effective except by a favorable vote of two-thirds (2/3) of all members of the city council.