Counting numbers are to be formed using only the digits \( 6,3,4,5,8,9,2 \), and 1 . Determine the number of different possibilities for two-digit numbers. \( \square \) numbers (Simplify your answer. Type a whole number.)

To form a two-digit number, we can choose the first digit and the second digit from the given digits \( 6, 3, 4, 5, 8, 9, 2, \) and \( 1 \). The first digit can be any of the 8 digits (since a two-digit number cannot start with 0, which is not in our set), and the second digit can also be any of the 8 digits. Thus, the total number of different possibilities for forming two-digit numbers is given by: \[ \text{Total possibilities} = (\text{choices for first digit}) \times (\text{choices for second digit}) = 8 \times 8 = 64. \] So, the total different possibilities for two-digit numbers is \( \boxed{64} \).