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Solutions
Six boxes: F, G, H, U, T, and Q
Number of marbles: 6, 25, 36, 60, 49 and 52
i) Box Q is placed at the top.
ii) Two boxes are placed between the boxes Q and U.
iii) The box which has 52 marbles is placed just above box U.
iv) Number of marbles in the box Q is a perfect square number but not 49.
Following are the possibilities we get,

v) Only two boxes are placed below the box which has 16 marbles.
This condition is not satisfied in case 3. So, it is eliminated.

vi) Box F is placed above the box T, which is placed just above box H.
vii) Box G is placed just below the box which has the maximum number of marbles.

viii) Difference between the number of marbles in box T and box Q is 13.
The above statement is satisfied only in case 1.
So the final arrangement is,

Q : 6 → Q = 62 (square root of the number of marbles )
T : 7 → T = 72 (square root of the number of marbles)
Thus, U : 16 → U = 42
Hence, '4' is the answer.