The problem asks to determine how many distinct three-digit numbers can be formed using the digits 4, 5, 6, 7, 8, and 9, where the resulting number is less than 900, and no digits are repeated.

Step-by-step approach:

1. Hundreds place: The number must be less than 900, so the digit in the hundreds place must be either 4, 5, 6, 7, or 8 (since 9 would make the number greater than or equal to 900). Thus, there are 5 choices for the hundreds place.

2. **Tens