A company purchases a one-year insurance policy on June 1 for $1,769. Determine the adjusting entry on December 31

You have to calculate the amount of insurance used for the period of Jun 1 to Dec 31, which will be for 7 months.

So take your amount of $1,769 times 7/12 equals your adjusting entry amount.

Your adjusting entry will be:
Debit Insurance Expense and Credit Prepaid Insurance for the amount calculated above.