The correct answer is option (C):
Geomancy
The correct answer is Geomancy. Geomancy specifically refers to the practice of divination, which is seeking to predict the future or gain insight, through means like interpreting patterns in the ground, or more broadly, the arrangement of things. In this context, the belief that arranging a home or office a certain way will influence good or bad luck aligns perfectly with the definition of Geomancy.
Eugenics is the study of hereditary improvement of the human race. Antiquary is someone who studies antiques or the past. Soothsaying refers to predicting the future, often through mystical or divinatory means. Astrology is the study of the movements and relative positions of celestial bodies interpreted as having an influence on human affairs and the natural world. While soothsaying and astrology could potentially relate to a belief in luck, geomancy is the most direct and specific substitute for the described belief concerning arranging a space to influence luck.