how can subnet 172.16.0.0

172.16.1.0 - 172.16.1.255. there's another 256, for a total of 512.

Throw a subnet mask in for each subnet of these blocks.

255.255.255.0 - 255.255.255.14

Or am I missing something here?

172.16.0.0 with a net mask of 255.255.254.0

That would give you
172.16.[0/1].x (172.16.0.x and 172.16.1.x in the same subnet)
172.16.[2/3].x (172.16.2.x and 172.16.3.x in the same subnet)
172.16.[4/5].x
172.16.[6/7].x
and so on.

It's more than 15 subnets (actually 128), but it's blocks of 500 each.

Another choice would be
172.16.0.0 subnet mask 255.255.240.0
That would give the requested 16 subnets, and each would have about 4000 available addresses within the subnet.
172.16.[0/7].x (172.16.0.x through 172.16.7.x in the same subnet)
172.16.[8/15].x (172.16.8.x through 172.16.15.x in the same subnet)
172.16.[16/23].x
172.16.[24/31].x
and so on.

So which are you really looking for - 512 addresses in each subnet, or 16 subnets within 172.16.x.x?

He gets an A+ for creativity.

The last couple of homework assignments my kid brought home and asked me about, I found the answer with Google. Just searched the first 3 or 4 relevant terms, and presto...

I should know, only geeks and college professors use the 172.16/12 prefix. Everyone else uses 192.168/16 or 10/8 :-)