The correct answer is B) breadth. The free surface constant of a tank carrying liquids is primarily determined by the breadth of the tank. This is because the free surface effect, which influences the vessel's stability, is directly related to the width of the liquid surface. The broader the tank, the greater the free surface effect and the higher the free surface constant. In contrast, the depth, length, or displacement of the tank are not the most important factors in calculating the free surface constant. The other answer choices are incorrect because they do not directly determine the free surface constant to the same degree as the tank's breadth.