What is the proper adjusting entry at June 30, the end of the fiscal year, based on a prepaid insurance account balance before adjustment, $15,500, and unexpired amounts per analysis of policies, $4,500?

Would you subtract 4500 from the 15500 to be your adjusting entry, making it 11000

The unexpired amount of $4,500 should be the amount that still is in the Prepaid account after the adjusting entry.

So you should do the adjusting entry for 11,000.

Deibt Insurance Expense for 11,000
Credit Prepaid insurance for 11,000