Final answer:
To administer free-flow oxygen, a nasal cannula should be used; this is the most appropriate and convenient method as it delivers oxygen directly to the nostrils. Options such as intramuscular or subcutaneous injections are not suitable for oxygen administration.
Step-by-step explanation:
To administer free-flow oxygen (O2), the appropriate method is c) Nasal cannula. This device is designed to deliver oxygen directly to the patient's nostrils, allowing for increased oxygen intake to assist with breathing. Other methods listed, such as intramuscular injection and subcutaneous injection, are not suitable for the administration of oxygen as they are used for delivering medications. Oral ingestion also does not apply to oxygen delivery. Oxygen administration pertains to the concept of pulmonary ventilation, which is the process of moving air in and out of the lungs to facilitate external respiration - the exchange of gases between the environment and the blood in the pulmonary capillaries.
Modalities such as intravenous or intramuscular injections are often reserved for medications, particularly when high plasma levels are required or when the drug is not effectively absorbed in the gastrointestinal tract. However, for delivering oxygen in a free-flow manner for home or hospital use, nasal cannula is convenient and effective as it provides a continuous flow of oxygen to meet the patient's needs.