this is what i found.
Multi-coating is very easy to see. Upon close examination of the filter; you will be able to discern several different colors: green, yellow and blue being the most common. The easiest way to check for multi coating is to get the reflection of a household light bulb in the filter. If the filter is multi coated the bulbs reflection will be radically changed.
Is My Filter Multi-Coated?
Multi-coated camera filters will reflect the reflected lamps image in many different colors (usually magenta and green tones), depending on the number and kind of optical coatings applied to the surface of the filter glass, just like most camera lenses. Mono-coated (single coated) camera filters will show a color tint change, but the color tint is harder to see. Non-coated camera filters will show no color tint change, of the bulb. To compare the reflections, use glass that is known not to be coated. use regular window glass or glass from a simple photo frame.
MultiCoated Camera Filters why they are worth the cost
How to Use Filters
How to Use Filters