A common type of water heater that incorporates an automatic gas-fired storage heater and features a single tank used for both heating and storing the water is the:

The correct answer, which identifies a water heating system that utilizes an automatic gas-fired mechanism with a single tank for both heating and storing water, is the direct hot water heater.

A direct hot water heater is designed to heat water directly as it is needed and store it for immediate use. This type of system typically involves a storage tank where water is heated and maintained at a specific temperature through gas burners. The design allows for a steady supply of hot water, making it a practical choice for many residential settings.

Other types of heaters mentioned, such as instant water heaters, focus on providing hot water on demand without a storage tank, which does not align with the description provided. Tankless water heaters also operate without a storage tank, heating water as it flows through the system. Solar water heaters, while they involve a different method of heating water using solar energy, typically include separate components and are not gas-fired. Therefore, the configuration of a tank that serves both heating and storage functions distinctly classifies the direct hot water heater as the correct choice.