The question asks for the order of the group $\mathbb{Z}_6$ under addition modulo 6.

Explanation:

1. The group $\mathbb{Z}_6$ consists of the integers $\{0, 1, 2, 3, 4, 5\}$ under addition modulo 6.
2. The order of a group is the number of elements in the group. Here, the group $\mathbb{Z}_6$ clearly has 6 elements.
3. Thus, the order of $\mathbb{Z}_6$ is $6$.

Correct Answer:

(B) 6

Would you like further details or have any additional questions? Here are some related questions you might find interesting:

1. What is the structure of $\mathbb{Z}_n$ under addition modulo $n$?
2. How does modular arithmetic ensure closure under group operations?
3. Why is $\mathbb{Z}_n$ always a cyclic group under addition modulo $n$?
4. Can $\mathbb{Z}_n$ have a subgroup under addition modulo $n$?
5. How do we prove that $\mathbb{Z}_n$ satisfies the group axioms?

Tip: When solving group theory problems, remember to always verify the set satisfies closure, associativity, the existence of identity, and inverses under the operation!