Host IDs

From that data (IP 150.17.0.0 and a subnet mask of 255.255.255.0) there are 254 standard subnets (255 if you use subnet-zero). The question asks for four subnets and the first four standard subnets would be:

150.17.1.0 (IP's 150.17.1.1-150.17.1.254)
150.17.2.0 (IP's 150.17.2.1-150.17.2.254)
150.17.3.0 (IP's 150.17.3.1-150.17.3.254)
150.17.1.0 (IP's 150.17.3.1-150.17.3.254)

And the last subnet would be:

150.17.254.0 (IP's 150.17.254.1-150.17.254.254)


All the subnet mask does is to specify what part of the IP is the network portion and what part is the host portion. If you convert both the IP and the subnet mask to binary quads and logically AND each quad the result is the network quad. In this case (it's simple) the network portion in 150.17.n and the host portion is 0.0.0.n.

255.255.255.0 uses 150.17.0.1 to 150.17.0.254 (classful routing, you lose network and broacast addresses).
We usually break something like that with 26 bit subnets (255.255.255.192)
..1 to .62
..65 to .126
..129 to .190
..193 to .254
Given that most of our sites are roughly the same size. You could break it up many different ways, though. Rewording what jlevie said, the subnet just defines how many IP addresses you can have "in that building". You can, of course, have many subnets in one physical building, it's just a good way to visualise it.
Can't remember where, but I downloaded a demo version of a subnet calculator at work. There's a few of them out there, and can be quite handy (saves doing the math in your head) and can be useful in teaching subnetting.