Final answer:
A subcutaneous injection is administered into the fat layer beneath the skin. For home administration of an antimicrobial for a systemic infection, the oral route is usually the most appropriate and convenient.
Step-by-step explanation:
The type of injection that is administered under the skin and into the fat layer is a subcutaneous injection. This method is used to deliver medications that require a slower release into the bloodstream. The corresponding answer in the provided options is c) Subcutaneous injection.
Regarding the most appropriate and convenient route of administration for home treatment of a systemic infection with an antimicrobial, the oral route, option A, is generally preferred. Oral administration is non-invasive and can be easily managed at home without the need for specialized equipment or training.