Answer should be 6, 7, 9.

Clue #1:
1, 4, 7 – One correct digit in the wrong position

Clue #2:  
1, 8, 9 – One correct digit in the correct position

Clue #3:
9, 6, 4 – Two correct digits with in wrong positions

Clue #4:
5, 2, 3 – All digits are incorrect

Clue #5:
2, 8, 6 – One correct digit in the wrong position

• From Clue #5, we can safely eliminate digits 2, 3, and 5 from all positions.
• Comparing Clues #1 and #2, we can eliminate digit 1 from all positions since the digit cannot be both in the right and wrong positions at the same time.
• Comparing Clues #2 and #5, we can eliminate digit 8 from all positions since the digit 8 cannot be both in the right and wrong positions at the same time. 
• Looking at Clue #3, since we have eliminated digits 1 and 8, this means that digit 9 is in the last position. 
• Looking at Clue #5, since we have eliminated digits 2 and 8, the correct digit in the wrong position must be 6.
• Looking at Clue #3, since we have established that digits 6 and 9 are correct, this means that we can eliminate digit 4.
• Looking at Clue #1, since we have eliminated digits 1 and 4, this means the last correct digit must be 7.
• From Clue #3, the digit 6 cannot be in the middle position, therefore, digit 6 must be in the first position.
• Digit 6 in first position, digit 7 in middle position, and digit 9 in last position.