How would I record an adjustment entry for dec.31st, If a business purchased a policy for 7,200 on October 1st?

You need to know how much of the policy was used during the period from oct 1 to Dec 31.

For example you purchase a one year insurance policy for $1,200 on Oct. 1.

The initial entry to record the transaction is:
Debit Prepaid Insurance for 1,200
Credit Cash for 1,200

to find out how much insurance was used you take the $,1200 X 3/12 (3 months/1yr policy).
The amount of insurance used is $300.

The adjusting entry is:
Debit Insurance Expense for 300
Credit Prepaid Insurance for 300