An ice cube is dropped into boiling water. How will heat flow between the water and the ice cube?

Heat transfers from hot body to cold body. So when ice is dropped in water, the water at higher temperature will lose heat energy and is gained by the ice at less temperature. When the Net heat lost equals to Net heat gained i. e., When both the bodies attain themal equilibrium, the flow of heat energy stops and both attain equal temperatures.

On a microscopic (molecular) level, heat flows from the ice to the boiling water

at a minuscule rate, and from the water to the ice at a humongous rate.