You are sitting in a boat on a lake, you have with you in the boat a large rock. You throw the rock out of the boat and it sinks to the bottom of the lake, does the water level of the lake go up, down or stay the same?

Whilst in the boat the rock (and you) are floating, this means that the amount of water displaced by the rock is the mass of the rock. When the rock sinks to the bottom of the lake the amount of water displaced by the rock is the volume of the rock.
As the rock sinks to the bottom of the lake, we know that the rock is more dense than water.
As the rock is more dense than water, the rock will displace more (a greater volume of) water when floating than when at the bottom of the lake. This means that after throwing the rock out of the boat the water level of the lake as a whole will go down.