Correct answer is D. Can someone explain why electrons would flow in to solution from the negatively charged cathode? I thought reduction always occurs at the cathode, instead of the cathode producing electrons to allow for reduction somewhere else (the solution).
You are correct, for both electrolytic, galvanic and concentration cells, RED CAT AN OX applies as well as saying that the electrons flow from anode to cathode. In a galvanic cell the cathode is + while in an electrolytic cell the cathode is - (eliminate choices B and C). Also in an electrolytic cell the reactions are no longer spontaneous and we must use electrical energy to drive the chemical reaction, so we will have electrons going where they normally would not want to go.
Read the Q carefully. It does not ask about the movement of electrons from one node to another (which would be from anode TO cathode), but rather the movement of electrons from one node to the solution surrounding it. Ask yourself, which node would need to give up electrons. In an electrolytic cell the Cathode is - and an external battery supplies the electrons that drive the battery. These electrons enter, via the battery through the cathode and come out through the anode. Take a look at the picture below of an electrolytic cell in action. The cathode needs to continually allow electrons to flow into it in order to facilitate the REDOX that drives the reaction.