In what situation can you be at rest and moving at the same time?
If you are stationary, but in/on a moving vehicle/object
If you are sat on a moving vehicle then you are at rest relative to the vehicle, but moving relative to the ground outside.
Even cooler, you are both at rest and moving right now - at rest relative to the earth, but because the earth is moving, moving relative to the rest of the solar system.
Hope this helps; let me know if I can do anything else:)