Final answer:
The Thermostatic Expansion Valve (D) is the most commonly used metering device, followed by capillary tubes, with automatic expansion valves and high-pressure float valves being less common.
Step-by-step explanation:
The metering device most commonly used in refrigeration and air conditioning systems is the Thermostatic Expansion Valve (D). This device adjusts the flow of refrigerant into the evaporator based on the refrigerant's temperature, thereby optimizing the system's efficiency. Capillary tubes (B) are also commonly used, especially in smaller systems, due to their simplicity and low cost. Automatic expansion valves (A) and high-pressure float valves (C) are less commonly used compared to the thermostatic expansion valve and capillary tubes.