"A customer calls a registered representative to sell 500 shares of an over-the-counter stock and tells the representative that he wants the trade done privately - not in the public market. This is:"

Not allowed, FINRA prohibits private securities transactions. Trading must be done with the knowledge of your firm in the public securities markets

Explanation:

Since in the question it is mentioned that call of the customer registered the representative for selling off  500 shares over the counter stock and the transactions should be done in privately

here according to the FINRA, it prohibits the transactions in which the person deals in private securities also there should be knowledge in the firm for the securities market held in market

i believe that it is a 45% chance.