The problem: Find the average of 12 numbers, given that the average of the first nine numbers is 21 and the average of the last three numbers is 17.

Approach:
To find the average of all 12 numbers, we need to calculate the sum of all 12 numbers and divide it by 12. We can utilize the given information to determine the sum of all the numbers.

Calculating the sum of the first nine numbers:
Since the average of the first nine numbers is given as 21, we can multiply this average by the number of elements to get the sum of these numbers. Therefore, the sum of the first nine numbers is 21 * 9 = 189.

Calculating the sum of the last three numbers:
Similarly, since the average of the last three numbers is given as 17, we can multiply this average by the number of elements to get the sum of these numbers. Therefore, the sum of the last three numbers is 17 * 3 = 51.

Calculating the sum of all twelve numbers:
To find the sum of all twelve numbers, we add the sum of the first nine numbers and the sum of the last three numbers. Therefore, the sum of all twelve numbers is 189 + 51 = 240.

Calculating the average of all twelve numbers:
Finally, to find the average of all twelve numbers, we divide the sum of all twelve numbers by the number of elements, which is 12. Therefore, the average of all twelve numbers is 240 / 12 = 20.

Conclusion:
The average of the twelve numbers is 20.

Answer:
The average of the 12 numbers is 20.