The correct answer is: B. assured
To assure someone means to tell them that something is true or will happen, in order to make them feel confident or less worried. In this case, the captain is trying to make the passengers feel less afraid by assuring them that there is no danger.
The other options are not as accurate. To promise something means to say that you will definitely do it. In this case, the captain is not making a promise, he is just trying to reassure the passengers. To advise someone means to give them advice, or to tell them what you think they should do. In this case, the captain is not giving advice, he is just trying to make the passengers feel less afraid. To counsel someone means to give them advice or guidance, especially on a personal or emotional matter. In this case, the captain is not giving counsel, he is just trying to make the passengers feel less afraid.