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Solutions
Eight boxes namely H to O are placed in a rack one above the other.
1. Three boxes are between the box O and the box M but the box O is above the box M.
Here we have four cases according to this Condition.

2. Box L is immediate above the box N but below the box M.
(Case III and Case IV not follows because in the question given box L and box N are below the box M but it is not possible in these cases)
Case I Splits into one more case i.e. Case I(a)

3. Four boxes are between the box L and the box J.
(Case I(a) and Case II not follows because in the question given Four boxes are between the box L and the box J but it is not possible in these cases)

4. Box K is above the box M and below the box J.
Again case I Splits into two more cases i.e. Case I and Case II

5. Box I is below the box K and above the box L.
Again case II Splits into one more case i.e. case II(a)

6. Two boxes are between the box I and the box H.
(Case II and Case II(a) not follows because in the question given Two boxes are between the box I and the box H but it is not possible in these cases)

Hence, box L is between the box N and the box I.