Final answer:
The organization with a class B network should use a subnet mask of 255.255.252.0 to create 64 department subnets, which allows for exactly 64 subnets by utilizing 6 additional bits for subnetting.
Step-by-step explanation:
If an organization with a class B network wants to create 64 department subnets, they need to choose an appropriate subnet mask that allows for at least 64 separate networks. Since a class B network has a default subnet mask of 255.255.0.0, which allows for 16,384 subnets (2 to the power of 14), we need to provide more bits to the subnet part of the mask to satisfy the requirement of 64 subnets.
The number of bits required can be found by calculating the minimum number of bits that will provide at least 64 options for networking, which is 6 (since 2 to the power of 6 is 64). Thus, we need to add these 6 bits to the default 16 bits of the host portion of the class B network's subnet mask. This leads to a new subnet mask of 255.255.255.192, which in binary is 11111111.11111111.11111111.11000000. However, this mask provides up to 256 subnets, which is more than required.
To allow exactly 64 subnets, you would use 2 bits from the third octet, giving a subnet mask of 255.255.252.0 (or /22, since 16+6=22 bits are used for the network and subnet, and 10 bits are left for the host addresses). This allows for exactly 64 subnets (2 to the power of 6).
Therefore, the correct answer is (b) 255.255.252.0.