Which IP address class has the capability of hosting approximately 16.7 million hosts?

The correct choice is Class A, which is designed to accommodate a vast number of hosts. In a Class A network, the first octet of the IP address (the first 8 bits) defines the network portion, while the remaining three octets (the next 24 bits) are available for host addresses. This setup allows for 2^24 (or 16,777,216) possible host addresses per Class A network.

The structure of Class A IP addresses ranges from 1.0.0.0 to 126.0.0.0, which supports a large number of devices and is suitable for very large networks. The capacity to directly connect millions of hosts is why Class A is typically utilized in environments requiring significant IP address assignments, such as major corporations and internet service providers.

In contrast, Class B can host approximately 65,536 hosts, and Class C can handle around 254 hosts, making them more appropriate for medium and small-size organizations, respectively. Class D is reserved for multicast addressing and does not utilize host bits in the same way, hence not applicable for hosting individual devices.