Think of this as picking the material that can trade its own sodium ions for the calcium and magnesium ions that make water hard.
Option A, silicones: these are Si-O based polymers used mainly for waterproof coatings, lubricants, and sealants because they repel water, they do not have any exchangeable ions built into their structure, so they play no role in softening water.
Option B, zeolites: these porous aluminosilicate minerals have loosely bound sodium ions sitting in their cage structure. When hard water flows through a zeolite bed, calcium and magnesium ions from the water swap places with those sodium ions and stay trapped in the solid, releasing soft, sodium rich water. This ion exchange behaviour is precisely why zeolites (permutit) are the standard material in domestic and industrial water softeners.
Option C, asbestos: this fibrous magnesium calcium silicate mineral is used for its heat resistant and insulating properties in older construction and brake linings, it is not used anywhere in the water softening process.
Option D, quartz: pure crystalline silica has a rigid, fully bonded lattice with no loosely held ions to exchange, so it cannot pull calcium or magnesium out of water.
Only zeolite offers the ion exchange mechanism that softening requires, so option B is correct.