Final answer:
Christine is asking Rhoda to look her in the eyes, which implies she is seeking truth and sincerity in Rhoda's response.
Step-by-step explanation:
In the dialogue, Christine is asking Rhoda to look her in the eyes and tell her something that she feels she needs to know. Christine's directive is seeking visual contact, which is commonly understood to be a gesture aimed at discerning truthfulness or sincerity in a person's statement. Therefore, the correct answer to what Christine asks Rhoda to do is to look her in the eyes.