Here's how I know how to do this problem. There may be a more "technical" way to do it, but my way will work.

If we have 5 digit zip codes that MUST start with either 7 or 8, then 4 of the 5 digits can be any arangment of 0-9. That's 10 digits that can appear in 4 slots = 10^4 = 10000, and 2 digits that can appear in the first slot, which is 2*(10000) = 20,000.

However, if I'm mistaken, I would appreciate someone coming to correct me.