Visual Demonstration?

The answer is (b). Instead of suspending the connecting bar, balance it on a pencil point. The bar won't feel any difference, but doing this emphasizes that the equilibrium is unstable, since if you unbalance the bar ever so slightly, it will tumble off the pencil point. But unbalancing is exactly what happens when you lower the arrangement into water: the lump of gold is more dense than the wreath, so the lump experiences less buoyancy, meaning a greater net downward force on the right side. This initiates a clockwise turning of the connecting bar. In the bottom picture, resolve the end force vectors into components along and perpendicular to the bar. The greater force perpendicular to the bar is still on the right, so the turning continues, and only when the chunk of gold is hanging straight down does the system attain stable equilibrium.

Another Way?

Archimedes' problem was to determine the wreath's density so it could be compared with the density of gold. Density being mass per volume, it would have been enough to weigh the wreath and to determine its volume. To get its volume, place it in a vessel and fill it to overflowing with water so that the wreath is completely submerged with no air bubbles clinging to it. Then remove the wreath, letting any excess water drip back in, and find how many units of volume it takes to return the bucket to overflowing.