The correct answer is D) posted in the pilothouse. The stability letter is a critical document that outlines the vessel's stability characteristics and operational limitations. According to Coast Guard regulations, the stability letter must be posted in a conspicuous location, typically the pilothouse, where the captain and crew can readily access and refer to it. This ensures that the vessel's stability information is readily available to the crew during operations, allowing them to make informed decisions and maintain the vessel's safe operation. The other options are incorrect because the stability letter should not be posted in a passenger area (A), as it contains technical information not intended for passenger viewing. It also should not be filed in the ship's office (C), as it needs to be readily accessible to the crew. Posting it adjacent to the Certificate of Inspection (B) is also not the correct location, as the stability letter is a separate document with its own specific posting requirements.