Anwer- B. 188.8.131.52/20
for n/w id, all the host id part should be 0. Since it has to support 4096 hosts, -> 2^12 => 12 bits represent host id.
Note- Here in question, it is mentioned to assign IP to 4096 hosts, so we would actually need 13 bits to support this many hosts.[ 1 for n/w id and another for broadcast]. But since, no option satisfies, therefore, it is obvious that they are neglecting these 2 addresses.So, consider 12 bits for host id.
Therefore, 32-12 = 20 bits represent n/w id. Now, we know the prefix-length, the remaining 12 bits should be all 0's which is only in option B.
Therefore this is the solution.