Question

S waves can travel for one side of the moon through the core to the other side what does this tell you about the center of the moon explain

Answer 1

S waves can travel from one side of the moon, through the core, to the other side because the moon's center is not a liquid, but a solid. S waves can't travel through liquids.
S waves can ONLY travel through solids.
Therefore, the inside of the moon must also be solid.