The question that you pose has 2 constraints (the solution must have at least 250 subnets and each subnet must support at least 250 hosts) and the successful solution must satisfy both of them. I would suggest that you start with one constraint, find a solution that satisfies that constraint and then check to see if that solution also satisfies the other constraint.
I would probably start with the constraint about how many hosts are supported in various subnets. There is an easy chart that you can work out to provide this:
CIDR notation subnet usable
(/ notation) mask hosts
/30 255.255.255.252 2
/29 255.255.255.248 6
/28 255.255.255.240 14
/27 255.255.255.224 30
/26 255.255.255.192 62
/25 255.255.255.128 126
/24 255.255.255.0 254
From this chart it is evident that you need a subnet with mask 255.255.255.0 (/24) to get the right number of hosts.
So then check to see if this solution also satisfies the other constraint. Since you were given a class B address, which uses 16 bits for the network part of the address, and you need to use 8 bits for the host part of the address,then it leaves you with 8 bits for the subnet part of the address. So how many subnets can you have with 8 bits for the subnet part of the address? The answer is just slightly more than 250.
So the answer to the question is that if you have network 126.96.36.199 you need to create subnets with /24 (255.255.255.0) to get the required number of hosts and required number of subnets.
I started by solving the constraint for number of hosts. You could just as easily start by solving for the number of subnets. And you should come out with the same answer either way.