Answer:
I believe the best answer is letter D. you ask for clarification of what the person is saying.
Step-by-step explanation:
If you stand motionless or stare down at the floor, as suggested in letters A and B, the speaker may feel as if you are just pretending to listen or as if you are not interested, respectively. Those approaches would certainly encourage them to stop talking instead. Now, if you continuously offer your opinion (letter C), you'll be constantly interrupting the speaker. Not only will he/she be annoyed, but such behavior may be considered rude and inadequate.
The best option is letter D. When you ask for clarification, you make it clear that, not only were you listening, but also paying attention. If you ask for clarification, that means the subject interests you. You are curious enough to want to know more about it. That will encourage the speaker to keep on discussing.