The correct answer is option 3: Principle of calorimetry. This principle states that the heat lost by one object is equal to the heat gained by another object when they are in thermal equilibrium.

Let`s analyze the other options to understand why they are not the correct answer:

Option 1: Principle of thermal equilibrium. While this principle is related to the concept of heat transfer, it does not specifically address the relationship between heat lost and heat gained. It states that when two objects are in thermal equilibrium, there is no net heat transfer between them.

Option 2: Principle of colors. The principle of colors has no direct relation to the concept of heat transfer or the equation heat lost = heat gained.

Option 4: Principle of vaporization. This principle is related to the phase change from a liquid to a gas and the heat energy required for this process. It is not directly linked to the equation heat lost = heat gained.

Therefore, option 3, the principle of calorimetry, is the correct choice as it directly addresses the relationship between heat lost and heat gained.