Final answer:
The Ptarmigan is the game bird that changes from a mottled grey and brown color in the summer to white in the winter to blend with its environment.
Step-by-step explanation:
The game bird that changes its color from mottled grey and brown in the summer to white in the winter is the Ptarmigan (choice B). This change is an adaptation to their environments, providing camouflage against the snowy backdrop during winter months and blending in with rocks and foliage during the summer. Unlike the Ptarmigan, the Snowy Owl does not change color; it remains primarily white year-round. The Mallard and the Turkey, while also types of birds, do not undergo seasonal changes in plumage color.