Finally... you must be wondering what the hell have I just told you?
You have green eyes, so what? Put on some red eye shadow and live happily ever after?
Weeeell... drug queens will definitely love it!))))

Look at the Color Wheel again.
Let's imagine that you have blue eyes, and if you use the same colour for your eyeshadow - you'll end up with a huge blue spot on your face. Blue blends with your beautiful eyes, it doesn't make your eyes bluer. The same with green. You can just take yourself a green skirt and a green shirt. How does it look like? Booooring.  Or how will you look like if you're dressed in jeans clothes? Shirt, jeans, jacket - everything of the same material. Horrible, people. That is horrible.

With the brown colour we are not usually competing.
Though, you might have a gold undertone, then burgundy, purples will bring it out.
Just look at the color wheel. The opposite colour of yellow is purple.
If you have darker brown eyes - purples, blues are your colours.

But what if you have hazel eyes? 
If they are green and blue - you can decide what colour you want to bring out.
For blue you choose all warm of shades. Brown, bronze, gold....
For green - purple, burgundy.

If they are green-blown hazel eyes - I would suggest bringing out the green colour. So we use burgundy, purples.

The point is - we go across!!!

So, here we are. I honestly tried to make it simple)))
I even have a dessert for those who managed to stay till the end;)))

(warm shadows)          
 copper, peach, bronze, coral, rust              
(cool shadows)
 pink, violet purple

(neutral shadows)
white, grey, caramel, gold, chocolate, silver

(evening shadows)
plum, burgundy, dark brown, black, cranberry, indigo

GREEN EYES (avoid white & silver)
 (warm shadows)                                                                                
 apricot, bronze, peach      
 (cool shadows)
lilac, pink, plum 
(neutral shadows)
soft brown, pink, mocha, fawn, +shimmery colours

 (evening shadows)
dark brown. violet, copper, burgundy


(warm shadows)    
gold, taupe, copper, coral 
(cool shadows)
lilac, lavender

(neutral shadows)
beige, pink, grey

(evening shadows)
eggplant, plum, violet, purple, emerald, dark blue, deep forest green

(warm shadows)      
 bronzecopper, orange, coral                                                                           

(cool shadows)
violet, soft silver, +glitter

(neutral shadows)
grey, beige, pink

(evening shadows)
purple, charcoal, metallic green