What did the man mean by “I've got some letters”?

The phrase “I've got some letters” implies that the man possesses letters, likely in a physical form or electronic format, that he intends to send or act upon. In this context, the most natural interpretation is that he plans to send mail, which is often associated with having letters ready to go out. This phrase commonly carries the connotation of being engaged in the act of mailing or communicating with others, whether it involves personal correspondence or professional communication.

While the other options could have some relevance depending on the broader context, they do not directly align with the most straightforward meaning of the phrase. For instance, while he may be writing letters (which is suggested by the option about writing), it does not specifically address the action of sending mail. Similarly, having responsibilities or being busy with work could indirectly relate to the idea of managing correspondence, but they do not explicitly reflect the content of the statement. Thus, the interpretation that he plans to send mail captures the essence of the phrase most accurately.