A pure Ameraucana rooster will be pure for the blue egg gene. He will give a copy of that dominant OO gene to each of his offspring. A pure Orpington hen will be pure for the white egg gene. She will give a copy of that recessive oo gene to each of her offspring. So each offspring will have Oo and pullets will lay a base blue egg.
A pure Ameraucana rooster will not contribute any brown shell color to any of his offspring. A pure Orpington hen will contribute brown shell color to all her offspring. So all offspring will receive some brown shell color to put on top of the base blue egg shell. That means a green egg. Exactly what shade of “green” is unknown. It could be pretty close to blue, maybe olive green, maybe minty green, or some other shade. It’s highly possible different pullets from that cross will lay different shades of green. It depends on what “brown” the Orpington contributes.
A pure Ameraucana rooster will not contribute any brown shell color to any of his offspring. A pure Orpington hen will contribute brown shell color to all her offspring. So all offspring will receive some brown shell color to put on top of the base blue egg shell. That means a green egg. Exactly what shade of “green” is unknown. It could be pretty close to blue, maybe olive green, maybe minty green, or some other shade. It’s highly possible different pullets from that cross will lay different shades of green. It depends on what “brown” the Orpington contributes.