From I and II we can say that C is second to the left of D, I is sitting second to the right of D, as we know that I and C are not adjacent to D.
From III, IV and IV we can say that B is sitting to the left of I and second left of H, who is to the left of G.
                         OR
B is sitting to the left of D and second left of H, who is to the left of IAlso we can say that A is either to the left of D or C and F is either to right of G or left of G.We can say from the above information E is either to the right of G or left of CThe two possible arrangements are as follows.Case(i):

Case(ii):


H is to the immediate left of G.i.e case(ii), E is sitting second to the right of G.

From the given information is known that F is the grandfather, of B and H is the wife of F.
C is the daughter of H and F, and G is the son of the H and F.
D is the daughter of E and G, B is the son of C and A
The final relationship is as follows.

From the given information and the relations obtained above we know that B and F, C and D, E and H are sitting in a position opposite to each other.Hence A and G are sitting in a position opposite to each other.
It is given that B is in a position opposite F and F is adjacent to his daughter 'C' and H is to the right of F. D is sitting between G and B. From the above information we have two possible cases.
Case(i): F is facing the centerCase(ii): F is facing away from the center
In case (i) we have F and H, G and E are facing the center, as couples are facing the same direction. The other four are facing away from the center, as it is given that four are facing the center and also it is satisfying the condition G and D are facing different directions.Case(i) is possible
In Case(ii) we have F and H are facing away from the center, G and E are facing the center. We can say that D is facing away from the center. As G and D are facing different directions, B is also facing away from the center.
The remaining two persons A and C are facing the center, as it is given that four are facing the center.
The possible final arrangement are as follows.

In case(i) A is facing away from the center and in case(ii) A is facing the center.

Given that the number of persons not facing the center of the table is less than five. Also, no two persons are facing the center of the table. So we can conclude that the persons sitting adjacent to each other face different directions.
Case(i)Let V face the center.
Given Q is to the right of V and P is opposite to T. Also W is third to right of R and is opposite U. Implies V is to the left of P.The arrangement is as follows.

Case(ii)Let V face away from the center. From the given clues we can say that V is to the left of P.The final arrangement is as follows.

S and U are not adjacent to each other.

From I and II we say that F is player and seated opposite D. It is given that G is sitting third left of the actor, then we have two possible arrangements. Also H is the actor.Case I: G is second to the left of F, who is left of Actor.Case II: G is sitting to the left of F, who is second left of Actor.Case III: G is second to the right of F, who is third left of Actor.Case IV: G is third to the right of F, who is third left of Actor.We can say that the actor is not opposite to the scientist and in II and IV it is given that B is a scientist and sitting adjacent to E.The above arrangement is not possible for case II and IV.Hence case II and IV is eliminated.Case III is eliminated as B is adjacent to E and it is not possible in this case.In case I, the above arrangement is E is to the right of the actor, who is to the left of the scientist.From III and IV we can say that C is not an actor and not adjacent to D, then C is to the left of F, who is player.Also we can say that G is a businessman, as it is given that C is sitting adjacent to businessman.In III, it is given that the engineer and the doctor are adjacent to each other. The possible arrangement is D is an Engineer and A is Doctor, as we know that A is not an actor, only option left A is a doctor. Now, we can say that E is a teacher as it is given that E is not a lawyer then only option for E is a Teacher and C is a lawyer.The final arrangement as follows:

G and the businessman is a correct combination.

From I and II we can say that C is second to the left of D, I is sitting second to the right of D, as we know that I and C are not adjacent to D.
From III, IV and IV we can say that B is sitting to the left of I and second left of H, who is to the left of G.
                         OR
B is sitting to the left of D and second left of H, who is to the left of IAlso we can say that A is either to the left of D or C and F is either to right of G or left of G.We can say from the above information E is either to the right of G or left of CThe two possible arrangements are as follows.Case(i):

Case(ii):


B is immediate right of C. i.e. case(i) F is sitting second to the left of E.

From (ii)P      TQ     QT       PP       US       SU       PFrom the last sentence of (ii), only one possibility remains:RT
Q
P
S
UNow, using (iii) and the above derived result:R        CT        E/BQ        AP         FS         B/EU         D

Total number of children = (7 + 4 + 2 + 3 + 5) = 21