Consider routing table of an organization’s router shown below: Which of the following prefixes in CIDR notation can be collectively used to correctly aggregate all of the subnets in the routing table?

To find the aggregated CIDR prefixes, let us determine the range of IP addresses represented by each subnet entry in the third octet (since the first two octets $12.20$ are identical):

1. Subnet 1:12.20.164.0 with mask 255.255.252.0 (/22)

   • Number of third-octet values $= 256 - 252 = 4$

   • Range: $12.20.164.0$ to $12.20.167.255$

2. Subnet 2:12.20.170.0 with mask 255.255.254.0 (/23)

   • Number of third-octet values $= 256 - 254 = 2$

   • Range: $12.20.170.0$ to $12.20.171.255$

3. Subnet 3:12.20.168.0 with mask 255.255.254.0 (/23)

   • Range: $12.20.168.0$ to $12.20.169.255$

4. Subnet 4:12.20.166.0 with mask 255.255.254.0 (/23)

   • Range: $12.20.166.0$ to $12.20.167.255$ (subsumed within Subnet 1)

Combining all subnets, the total address space spans from $12.20.164.0$ to $12.20.171.255$ (a total of $8$ consecutive blocks in the third octet: $164$ through $171$):

• The block $12.20.164.0$ to $12.20.167.255$ forms the CIDR block 12.20.164.0/22 (Option B).

• The block $12.20.168.0$ to $12.20.171.255$ forms the CIDR block 12.20.168.0/22 (Option D).

Together, they collectively aggregate all the subnets.

• Option A (12.20.164.0/20) and Option C (12.20.164.0/21) are invalid CIDR prefixes because $164$ is not a valid starting boundary for $/20$ (multiple of $16$) or $/21$ (multiple of $8$).

Therefore, options B and D are correct.