Final answer:
Most appropriately, a sales associate should tell a customer that a shoe size is unavailable and suggest alternative sizes or styles. Providing false information is unprofessional and recommending another store may be a last resort after trying to fulfill the customer's need in-store.
Step-by-step explanation:
The most appropriate response to the customer's request when a certain shoe size is unavailable would be to kindly inform the customer that the size they are looking for is out of stock, which corresponds to option A. However, it is also good customer service to offer alternative options. Therefore, the associate should also do option B, suggesting a different size, if a close alternative might suit, or different style that is available in the customer's size.
It is not professional to provide false information, so option C should be avoided at all costs. While recommending another store, option D, is also a possible solution, it should perhaps come after suggesting different sizes or styles within the same store, as it is in the store's best interest to keep the customer's business if possible.