I just started networking and was given this exercise I'm trying to determine how many subnets are needed for this network.:

The main network ID is 192.168.0.0/16. Given that I know that this is a class B IP address and the subnet mask is 255.255.0.0. Based on my calculations maximum number of subnet with the given information is 11. But since I have 4 routers and 6 switches, I won't need more than 10 subnets. To achieve this should I change the network id to 192.168.0.0/28 which will give me a subnet mask of 255.255.255.240 where I will get 14 maximum number of hosts. Is my logic correct or am I missing something?