A750g aluminum pan is removed from the stove and plunged into a sink filled with 10.0kg of water at 20.0c. the water temperature quickly rises to 24.0c. what was the initial temperature of the pan

The concept that should be used here is that heat loss is equal to heat gain. In this item, the heat lost by the aluminum pan should be equal to the heat gained by water. Such that,
              750 g(0.215 cal/g°C)(T - 24) = (10000 g)(1 cal/g°C)(4°C)

The value of T from the equation is equal to 272°C.