[hddqsb]

Sure! (My explanation is basically equivalent to the combined explanations by @mafuy and @malcolp, but I'll post it anyway.)

The idea is to balance a scale with the crown on one side and an equal mass of gold on the other side (no water yet), and then submerge the entire scale in water. Now there will still be the same mass on each side, but there will additionally be a buoyancy force on each side proportional to its volume. So if the volume of the crown is different from the volume of the reference gold, the buoyancy forces will be different and the scale will tip.