What word would appropriately complete this sentence: What do you mean _____ that?

The correct choice for completing the sentence is "by." The phrase "What do you mean by that?" is a common expression used to ask someone for clarification on what they have just said. The preposition "by" in this context indicates the manner or method of something, prompting the speaker to elaborate on their meaning or intent.

In contrast, using "about" would suggest a discussion regarding a topic, which would not convey the same request for clarification on someone's specific language or statement. The prepositions "with" and "for" also do not fit grammatically or contextually in the same way, as they would alter the focus of the question and not effectively convey the speaker's intent to seek clarification.