To determine the seating arrangement of the eight persons around the circular table based on the given conditions, we can start by noting the positions step by step:

1. Initial Setup:

   • Let’s place $B$ and $D$ with two persons between them. Since it’s a circular table, there are two possible setups for $B$ and $D$:

     • $B$ - _ - _ - $D$
     • $D$ - _ - _ - $B$

2. F’s Position Relative to D:

   • $F$ is sitting 2nd to the left of $D$. So, if $D$ is at position 1, then $F$ would be at position 7.

     • $D$ - _ - _ - _ - _ - _ - $F$

   • If $D$ is at position 3, then $F$ would be at position 1.

     • _ - _ - $D$ - _ - _ - _ - $F$

3. One Person Between F and C:

   • If $F$ is at position 7 and one person is between $F$ and $C$:

     • $D$ - _ - _ - _ - _ - _ - $F$ - _ - $C$

   • If $F$ is at position 1 and one person is between $F$ and $C$:

     • $C$ - _ - $D$ - _ - _ - _ - $F$

4. G’s Position Relative to A:

   • $G$ is sitting 2nd to the left of $A$.

5. A is Not an Immediate Neighbor of F:

   • If $F$ is at position 7, $A$ could be at position 5 or 9 (which is equivalent to position 1).
   • If $F$ is at position 1, $A$ could be at position 8 or 3 (which is $D$).

6. H’s Position Relative to B:

   • $H$ is not sitting adjacent to $B$.

7. Neither H Nor E is Opposite to G:

8. Two Persons Not Sitting Between G and F, Counted From the Left of G:

Using these constraints, we can place each person step by step.

Let’s place $D$ and $F$ first:

• $D$ at position 1, $F$ at position 7:

$(1) D - (2) - (3) - (4) - (5) - (6) - (7) F$

Next, we place $C$:

• $F$ at position 7, one person between $F$ and $C$:

$(1) D - (2) - (3) - (4) - (5) - (6) - (7) F - (8) - (9) C$ (Note that position 9 is equivalent to position 1, so position 8 for $C$).

$(1) D - (2) - (3) - (4) - (5) - (6) - (7) F - (8) C$

Next, $A$ and $G$:

• $A$ should not be immediate neighbor of $F$ and $G$ is 2nd to the left of $A$:
• Suppose $A$ at position 5, $G$ would be at position 3.

$(1) D - (2) - (3) G - (4) - (5) A - (6) - (7) F - (8) C$

• This doesn’t violate any conditions yet.

Now let’s place $B$:

• $B$ and $D$ have two persons between them:

$(1) D - (2) - (3) G - (4) B - (5) A - (6) - (7) F - (8) C$

Finally, $H$ and $E$:

• $H$ is not adjacent to $B$ and neither $H$ nor $E$ are opposite $G$:

So $H$ can be at position 6 and $E$ at position 2.

Final arrangement: $(1) D - (2) E - (3) G - (4) B - (5) A - (6) H - (7) F - (8) C$

This satisfies all the given conditions.

Would you like any specific details or have any questions?

Here are five more questions you might want to ask:

1. Can you explain how you determined the positions of $G$ and $A$?
2. What would be a different possible arrangement if there is any?
3. Can you provide a step-by-step explanation for each constraint?
4. How do the conditions “not sitting opposite” affect the arrangement?
5. Can you show the reasoning for placing $H$ and $E$ last?

Tip: When solving seating arrangement problems, drawing a diagram and labeling the positions can be very helpful.