In which of these substances are the molecules probably moving most quickly?

solid iron at −45°c
solid iron at 300°c
liquid iron at 1600°c
liquid iron at 1800°c

The substance with molecules that are probably moving most quickly is liquid iron at 1800°C. This is because the particles of the liquid iron can move or slide past each other due to the small space available for movement. It cannot be compressed further due to the repulsive forces that acts between them. And also, the temperature is increases which causes for more thermal vibration of atoms.

Crust,mantle,core,earth