Final Arrangement:

Boxes
E
B
C
F
D
G
A

Clues: Only two boxes are kept between box A and box F. Box B is kept two boxes above box F.

Inference: We have two possible cases:

Case 1 Boxes	Case 2 Boxes
B	A
	B
F
	F
A

Clues: Only three boxes are kept between box B and box G. The number of boxes kept above box G is one more than the number of boxes kept below box C. Box D is kept two boxes below box C.

Inference: Above clues are arranged in both cases.

Case 1 Boxes	Case 2 Boxes
	A
B	B
C	C
F	F
D	D
G	G
A

Clue: Box E does not kept below box D.

Inference: Case 2 gets eliminated here.

Case 1 Boxes	Case 2 Boxes
E	A
B	B
C	C
F	F
D	D
G	G
A	E

Inference: The final arrangement is:

Boxes
E
B
C
F
D
G
A

If box F is related to box E and box G is related to box C in the same way box D is related to box B.

The correct answer is Box D.

To find the correct relationship, let us first list the final vertical arrangement of the boxes from top to bottom based on the provided puzzle:
1. Box E (Top-most position)
2. Box B
3. Box C
4. Box F
5. Box D
6. Box G
7. Box A (Bottom-most position)

Now, let us analyze the pattern of relationship described in the question:
• Box F is related to Box E: Box F (4th position) is placed exactly 3 positions below Box E (1st position). There are 2 boxes (B and C) between them.
• Box G is related to Box C: Box G (6th position) is placed exactly 3 positions below Box C (3rd position). There are 2 boxes (F and D) between them.

Following this identical pattern, we need to find which box is related to Box B (2nd position) in the same manner:
• The box related to Box B must be placed exactly 3 positions below Box B.
• Counting 3 positions down from Box B (2nd position):
$2\; +\; 3\; =\; 5$
• The box at the 5th position is Box D (with exactly 2 boxes, C and F, between B and D).

Thus, Box D is related to Box B in the same way.