Calculate how much segements the system can handle
I think neither of those is a good solution, but yours is better than the one you were given.

Here's how I'd reason through it: there are 3 hex digits to represent the segment identifier.  That's 12 bits for the segment identifier.  12 bits can identify up to $2^{12}$ possibilities.  So the system can have at most $2^{12}$ possible segments.  The rest of the information is irrelevant.