D) On the other hand
Think about that phrase.
Imagine you are wearing a bracelet on your left hand and another on your right. You just got them, and you're really excited to tell your friend about them, so you call said friend and describe them to him/her. You go into detail about the one on your left hand and eventually run out of things to say, so you then say, "and on my other hand..." and begin describing that one. Its texture, color, design maybe.
This is taking that phrase in a literal way rather than the way it's used when it's a transitional phrase, however, thinking about it in this way may help you to remember that it is, in fact, introducing a comparison between two items, scenarios, etc.
Thank you for taking the time to read my answer, I hope it helped you to understand this topic a little better, and I hope the rest of your day is brilliant! Best of luck on your educational journey!