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

Step 1 ：We have 6 different digits that we can use to form a two-digit number. The first digit can be any of the 6 digits, and the second digit can also be any of the 6 digits. Since the digits can be repeated, we simply multiply the number of choices for the first digit by the number of choices for the second digit to get the total number of two-digit numbers.

Step 2 ：\(num\_digits = 6\)

Step 3 ：\(num\_possibilities = num\_digits \times num\_digits = 36\)

Step 4 ：Final Answer: The number of different possibilities for two-digit numbers is \(\boxed{36}\).