For network 172.16.0.0, choose a subnet mask that supports eight subnets while maximizing hosts per subnet.

Introduction / Context:
Subnet design for a class B private network (172.16.0.0/16) often optimizes for a required number of subnets while preserving large host counts per subnet. Here, exactly eight subnets are required, and host capacity should be maximized.

Given Data / Assumptions:

• Base network: 172.16.0.0/16 (class B).
• Required subnets: 8.
• Goal: maximize hosts per subnet.

Concept / Approach:
For a class B /16, there are initially 16 host bits. Borrow n bits for subnetting where 2^n = number of subnets. Keep n minimal to maximize remaining host bits. Hosts per subnet = 2^(remaining host bits) - 2.

Step-by-Step Solution:

Verification / Alternative check:
Subnet increments in the third octet are 32 (224 mask), yielding subnets starting at 172.16.0.0, 172.16.32.0, 172.16.64.0, etc., providing eight or more distinct subnets with large host ranges, which satisfies the requirement.

Why Other Options Are Wrong:

• 255.255.192.0 (/18): 4 subnets if counting by borrowed bits from /16, not enough for 8.
• 255.255.240.0 (/20): 16 subnets, but hosts per subnet are smaller than with /19; not maximizing hosts.
• 255.255.248.0 (/21): 32 subnets with even fewer hosts per subnet.
• 255.255.255.0 (/24): 256 subnets but very small host capacity per subnet compared to /19.

Common Pitfalls:
Forgetting classful starting prefix; miscounting borrowed bits; mixing up /18 vs /19; ignoring the maximize-hosts requirement and choosing a longer prefix than needed.

Final Answer:
255.255.224.0