At which distance can you keep someone "at arm's length"? select one: a. intimate b. personal c. social d. public

Personal. Personal space is the distance you may have when conversing with someone. What is considered personal space varies for males and females.
The best representation for public space is an audience. 
We keep intimate space with someone we now very well (partner, kids, relatives, and so forth).

I really think that keeping people at arms length is about social behavior and etiquette. The diversity in our country requires that we understand some cultural distances in communication. Using arm's length as your reference helps you not to invade anyone's personal space. It's universal.

Personal space references "our own" need for space in during communications.

Intimate space is determined by the couple themselves.

Public space cannot be controlled, while in the public, everyone is equal.

Read your textbook to answer that question