Even digits= 2,4,6..
Now,
3rd place will be filled by = 3 ways,
2nd place will be filled by = 6 ways,
1st place by = 6 ways,
Total number of ways= 6×6×3 = 108

Counting 3-Digit Even Numbers
To form a 3-digit even number using the digits 1, 2, 3, 4, 5, 6 with repetition allowed, we need to consider the following:

Even Number Property
- An even number has its last digit as 2, 4, or 6.
- Therefore, to form a 3-digit even number, the last digit must be one of these even digits.

Determining the Number of Possibilities
- First Digit: Since the number has to be 3 digits, the first digit cannot be 0. So, we have 5 choices (2, 3, 4, 5, 6) for the first digit.
- Second Digit: Any of the 6 digits can be used in any position, so we have 6 choices for the second digit.
- Third Digit (Even): Since the number must be even, we can only choose from 2, 4, 6, giving us 3 choices for the third digit.

Calculating Total Number of Possibilities
- To find the total number of 3-digit even numbers that can be formed, we multiply the number of choices for each digit position: 5 choices for the first digit, 6 choices for the second digit, and 3 choices for the third digit.
- Total possibilities = 5 x 6 x 3 = 90
Therefore, 90 different 3-digit even numbers can be formed using the digits 1, 2, 3, 4, 5, 6 with repetition allowed.