What word completes the statement: "ask him _____ You don't want everybody knowing your business."?

The appropriate word to complete the statement is "discreetly." This term embodies the idea of handling a situation with care and confidentiality. When asking someone not to share sensitive information, using the word "discreetly" implies that the action should be taken surreptitiously and with consideration for privacy. It suggests that the request should be made in a manner that is not public or obvious.

In contrast, the other options do not convey the same sense of privacy and tact. "Openly" suggests a lack of secrecy, which contradicts the intention of keeping one's business private. "Aggressively" implies a confrontational tone, which is inappropriate for a situation that calls for discretion. "Casually" indicates a laid-back or ignored approach, which doesn't align with the need to be careful about sensitive information. Thus, "discreetly" is the most fitting choice to express the desired level of caution and confidentiality.