Final answer:
Confirmations with suppliers most likely help an auditor determine whether accounts payable have been misstated by providing direct external verification of the reported figures with third-party records, thus ensuring their existence and accuracy.
Step-by-step explanation:
The test of details that would most likely help an auditor to determine whether accounts payable have been misstated is c. Confirmations with suppliers. This audit procedure involves sending confirmation letters to the entity's suppliers to verify the amounts owed as of the balance sheet date. This direct external verification helps in establishing the existence and accuracy of the reported accounts payable.
Confirmations with suppliers are particularly useful in detecting both overstatements and understatements of liabilities. It serves as proof that the amounts reflected in the financial statements agree with the records of third parties. Other procedures like analytical procedures might be used for preliminary assessments or in conjunction with confirmations, but they are less likely to provide the direct evidence that confirmations do. Inquiries of management and substantive analytical procedures are typically less conclusive and are used as complementary procedures rather than as primary means of verifying account balances.