Explanation:

Statement I: Scientific research, particularly from NASA and other geodetic studies, confirms that the Earth's rotational axis (polar motion) and even its rotation speed are influenced by mass redistribution on the planet, including the melting of glaciers and ice sheets, and changes in groundwater storage. This statement is correct. Statement II: Solar flares and coronal mass ejections (CMEs) are indeed powerful events that bombard Earth's outer atmosphere with energy. They cause geomagnetic storms, aurorae, and can affect satellites and power grids. However, they do not significantly or directly cause the long-term shifts in Earth's rotation and axis that Statement I refers to. While the statement about bombardment is factually correct, it does not explain Statement I. Statement III: As polar ice melts, the water flows into the oceans and redistributes towards lower latitudes (the equator). This shift in mass away from the poles increases the Earth's moment of inertia, which, by conservation of angular momentum, causes a slight slowing of Earth's rotation and a shift in its rotational axis. This is a well-established geophysical phenomenon. This statement is correct and directly explains a major mechanism behind the shift mentioned in Statement I. Explanation: Both Statement II and Statement III are factually correct statements. However, only Statement III provides a direct and scientifically accepted explanation for the shift in Earth's rotation and axis mentioned in Statement I. Statement II describes a different phenomenon related to solar activity, which does not explain the Earth's axial shift. Therefore, both Statement II and Statement III are correct, but only Statement III explains Statement I.