Let me try to explain, not replace the provided answer. Hope it helps.
In Set-up X, evaporation at the water surface takes place easily, without the layer of oil. This means the air above the water is constantly filled with water vapour as hot water evaporates. Condensation of the water vapour thus allows more space to be created for more evaporation of the hot water.
In Set-up Y, the above cycle is disrupted because the layer of oil prevents evaporation. As the water vapour already present above the oil layer condenses into water droplets, the amount of water vapour left decreases. This is seen as fewer and fewer water droplets condense on the metal cover.