Analyze the constraints:

• There are seven boxes arranged vertically (one over the other). Let's number the positions from 1 (bottom) to 7 (top).
• Constraint 1: "No box is kept below F." This means F is at the bottom position. $F = Position 1$.
• Constraint 2: "Only two boxes are kept between H and F." Since F is at Position 1, H must be at Position 4. $H = Position 4$. The arrangement so far is:

  7:	_
  6:	_
  5:	_
  4:	H
  3:	_
  2:	_
  1:	F

  
  

• Constraint 3: "E is kept at some place below S but at some place above U." This gives the order $S > E > U$ (S is above E, E is above U).
• Constraint 4: "Only G is kept above T." This means G is somewhere above T ($G > T$).

Deduce the arrangement:

• The available positions are 2, 3, 5, 6, 7.
• The remaining boxes are E, G, S, T, U.
• We need to place E, G, S, T, U satisfying $S > E > U$ and $G > T$.
• Consider placing U. U cannot be at Position 3 because that would require E and S to be placed above H (in positions 5, 6, 7), leaving only positions 2 for T and G, which violates $G > T$.
• Let's place U at Position 2. $U = Position 2$.
• Now, place E and S according to $S > E > U$. E must be above Position 2, and S must be above E. Available slots are 3, 5, 6, 7. Let's try placing E at Position 3 and S at Position 5. $E = Position 3$, $S = Position 5$.
• The arrangement is now: F(1), U(2), E(3), H(4), S(5), _, _.
• The remaining boxes are G and T for positions 6 and 7.
• Apply $G > T$. G must be at Position 7 and T at Position 6. $G = Position 7$, $T = Position 6$.
• This arrangement violates the constraint G > T (we placed T=6, G=7). Let's swap T and G. T=7, G=6? No, G must be above T. Let's reconsider placing E and S.
• Revising placement: Let U=2. For $S > E > U$, let's try placing E=3 and S=5. Slots 6, 7 remain for G, T. $G>T$ means G=7, T=6. Stack: F, U, E, H, S, T, G. Let's check constraints.
  • F=1 (Ok)
  • H=4, F=1, boxes U(2), E(3) between (Ok)
  • $G>T$? G=7, T=6 (Ok)
  • $S>E>U$? S=5, E=3, U=2 (Ok)
  This arrangement is:

  7:	G
  6:	T
  5:	S
  4:	H
  3:	E
  2:	U
  1:	F

  
  

• Answer the question: Which box is kept third above U?
• U is at Position 2.
• The box 1st above U is at Position 3 (E).
• The box 2nd above U is at Position 4 (H).
• The box 3rd above U is at Position 5 (S).

Therefore, S is the box kept third above U.