Final answer:
The primary centers of New Zealand cricket are Auckland, Wellington, and Christchurch, which is the correct answer to the student's question.
Step-by-step explanation:
The main centers of New Zealand cricket are located in its largest cities, which include Auckland, Wellington, and Christchurch. Auckland, with a population of 1.45 million people, is the primary city of New Zealand and located in the north. Wellington is the capital city and is situated on the southern coast of the North Island.
Christchurch is the largest city in the South Island, located along the eastern seaboard on the productive Canterbury Plain. These major cities not only serve as centers for sports but also play pivotal roles in the country's economy and transportation systems due to their coastal locations. Option (a) Auckland, Wellington, and Christchurch is the correct answer to the question.