Class B networks range from 128-191 (or 64 possible values) over their first 8 bits. Therefore, the number of networks had class B used 20 bits to represent the network part of the address would have been 64 * 212 = 262,144
Another way around this is that there are 2 [number of network bits - 2] addresses. We subtract 2 because Class B address must start with 10 (in binary). Thus there are 218 = 262,144 networks.