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 using the digits \( 6, 3, 4, 5, 8, 9, 2, \) and \( 1 \), we need to consider that the first digit cannot be zero and must be selected from the available digits, and the second digit can be any of the given digits. We have a total of 8 digits ( \( 1, 2, 3, 4, 5, 6, 8, 9 \) ) to choose from: 1. **First Digit**: We can choose any of the 8 digits (all are allowed). 2. **Second Digit**: We can also choose any of the 8 digits (repetition is allowed). To find the total number of different two-digit combinations: - The first digit has 8 choices. - The second digit also has 8 choices. So, the total number of different two-digit numbers that can be formed is: \[ 8 \times 8 = 64. \] Hence, the number of different possibilities for two-digit numbers is \( \boxed{64} \).