Nail polish remover is a volatile liquid mixture (typically acetone, sometimes with ethyl acetate, water, and fragrance additives). To count the number of components, you need a technique that can separate and detect volatile, small-molecule liquids with high resolution.

• Gas chromatography (GC) vaporizes the sample and separates components based on their differential partitioning between a mobile gas phase and a stationary phase. Each component elutes at a different retention time, producing a distinct peak. The number of peaks equals the number of components, making GC ideal for volatile liquid mixtures like nail polish remover.
• Paper chromatography works well for non-volatile, polar solutes (like ink or plant pigments) that can be adsorbed and separated on paper via capillary action, but volatile organic solvents evaporate too quickly and don't interact well with paper, giving poor separation.
• Boiling point determination only gives one temperature (or a range) for the whole mixture; it can't resolve multiple components unless they're fractionally distilled, and even then, azeotropes and close boiling points cause overlap.
• Combustion analysis determines elemental composition (%C, %H, %O, etc.) of a sample, not the number of distinct components in a mixture.

Therefore, GC is the appropriate method.