S-waves (shear waves) can only travel through solid materials and cannot pass through liquids. Given the Earth's layers:
- Outer Core: This layer is liquid, so S-waves cannot travel through it.
- Inner Core: This layer is solid, so S-waves can travel through it.
- Mantle: This layer is mostly solid, allowing S-waves to travel through it as well.
- Crust: This is also solid, so S-waves can travel through it.
Based on these properties, S-waves can travel through the inner core, mantle, and crust.
So the correct answer is: inner core, mantle, and crust.