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Question:

You are turning right on a red signal at this intersection. Just as you are about to turn, a pedestrian begins to cross the road you want to enter. What should you do here?

A Stop and let the pedestrian cross.
Explaination

You must stop and yield to all vehicles and pedestrians before turning right on a red light. You should always yield to a pedestrian in a crosswalk. [Right-of-Way, Traffic Control Laws, Section Four - Rules of the Road, Delaware Driver Manual]