I’m just going to . . . . . . . . post office behind my house. I won’t be long. A. a B. an C. the D. no article

The correct answer is: no article.

The post office is a specific place, so we do not need an article. We would use an article if we were talking about a general post office, or if we were not sure which post office we were talking about. For example, we could say “I’m going to the post office to mail a letter.” or “I’m going to a post office to buy some stamps.”

In this case, the speaker is going to a specific post office that is behind their house. They know which post office they are talking about, so they do not need an article.