Why do red curtains appear red when you shine a mixture of red and green light on to them?

Red curtains appear red when illuminated with a mixture of red and green light because they reflect the red component of the light while absorbing the green component. The pigments in the curtains are designed to absorb certain wavelengths of light, and since they absorb green light, only the red light is reflected back to our eyes. This selective reflection is what makes the curtains appear red, even in the presence of green light.