To find the intersection of T and N, we need to find the numbers that are common to both sets.
T is the set of even numbers from 1 to 12, so T = {2, 4, 6, 8, 10, 12}.
N is the set of common factors of 6, 8, and 12. To find the common factors, we can list the factors of each number and look for the factors that they have in common:
Factors of 6: 1, 2, 3, 6
Factors of 8: 1, 2, 4, 8
Factors of 12: 1, 2, 3, 4, 6, 12
The common factors of 6, 8, and 12 are 1, 2, and 3.
Therefore, the intersection of T and N, written as T ∩ N, is the set of numbers that are in both T and N. In this case, the only even number that is also a common factor of 6, 8, and 12 is 2. So, T ∩ N = {2}.
Therefore, {2} is the correct answer.