What type of boxes should be used only with cable wiring methods that have nonmetallic sheaths?

The correct answer centers around the specific application of nonmetallic sheathed cables, commonly known as NM cable. Nonmetallic boxes are designed to be compatible with NM cable, as they provide the right environmental and electrical insulation properties needed to protect the conductors within.

These boxes are made from materials that are non-conductive and can accommodate the cable's characteristics without introducing risks of electrical shorts or grounding issues, which could arise from using metal boxes. Additionally, nonmetallic boxes are typically lighter and easier to work with when dealing with the installation of nonmetallic sheathed cable. They are also constructed to allow for better support and anchoring of the sheath, ensuring a secure fit that complies with electrical codes.

While metallic boxes can be used with various types of wiring methods, they are not suitable for nonmetallic sheathed cables, as they can create potential for grounding problems. Wooden boxes may not provide the necessary protection and are often not used in modern electrical installations due to combustible materials. Plastic boxes, while also nonmetallic, do not specifically emphasize the design compatibility with the NM cable as strongly as nonmetallic boxes do, thus making the latter the preferred choice for installations involving nonmetallic sheathed cables.