This is my way of drawing eyes. It may not be for everybody and this isn't the "correct" way to draw eyes.
1. Sketch the eye and the eyebrow. Add the base color (separate layers).
2. Add the color of the pupil, the eyebrow and the whites of the eyes. Don't use white but a warm grey for the whites of the eyes. And add some shadows.
3. and 4. Add more shadows until you're satisfied.
5. Add some highlights. Change the color of the sketch layer from black to brown and set the layer to multipy. Merge the sketch layer and the color layer.
6. I increased the saturation because I found the colors too muted.
7. Blend the colors, clean up unnecesarry lines and and details.
8 Add the final highlights.
I hope this quick tutorial helped you!
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