Height difference and base molding

Q: Our kitchen and family room share a wall. We installed stone flooring in the kitchen and pergo flooring in the family room. As a result, the kitchen floors are slightly higher. We placed a transition on the ground to cover up the difference in height, but now we are unsure how to put up the base molding different heights.

Any suggestions?

A: I think you should have installed the quarter round first, if I am understanding your question correctly. Do you think it would be possible to gently remove the transition strip without breaking it?

Follow-up: Here is a cross-section while looking at the wall that the molding will go on.

A: Ideally, 2 dissimilar floor surfaces should stop in the middle of the door jamb or wall and if their is a door they should stop under the door. Then any transition strips installed would be in the middle of the doorway and not protrude beyond and into the room. Could you send me a photo?