The fact that a refrigerator requires energy to move heat from a colder object (the inside of the refrigerator) to a hotter object (the outside of the refrigerator) is a real life observation of which law of thermodynamics?

Clausius statement of the Second Law of Thermodynamics.

Explanation:

The fact that refrigerator requires energy to move the heat from a colder reservoir to a hotter reservoir is a real life observation of the Clausius statement of the Second Law of Thermodynamics.

Clausius statement tells that it is impossible to construct a device operating in a cycle that transfer heat from a low temperature reservoir to a higher temperature reservoir without consuming any work.