A Crudely written explanation:
738 nothing correct with 682 one correct means 8 is false and either
(i) 6 is correct
(ii) 2 is correct
If (i) or 6 is correct, it contradicts picture 614
Thus (i) is false and (ii) Is correct meaning last number must be 2.
Next in 206, 6 is false implies 2 and 0 are both correct. We know 2 is in last place so 0 must be in first place.
Next in 614, we know 6 is false by earlier argument thus either 1 or 4 is correct. But 1 cannot be correct because because it cannot be in the middle since first & last number is already 0 and 2 respectively. So 4 must be correct and only place for it is in the middle.
Giving answer 042