Final answer:
In Z12×Z6, there are 2 elements of order 6.
Step-by-step explanation:
In order to find the elements of order 6 in Z12×Z6, we need to consider the order of the elements. The order of an element (a,b) in Z12×Z6 is the least positive integer n such that (a,b)n = (0,0). In this case, we need to find the elements (a,b) such that n = 6.
Since the order of (a,b) is the least common multiple of the order of a and the order of b, we need to find the elements (a,b) such that the order of a is 6 and the order of b is 1 (since the order of any element in Z6 is 1).
By considering the elements of Z12, we find that there are 2 elements of order 6 in Z12. Therefore, there are 2 elements of order 6 in Z12×Z6.