It is given that, 
Eight persons  -  A, B, C, D, E, F, G and H are sitting in a linear row, but not necessarily in the same order. 
All are facing in the north direction.
From statement I alone: 
B, who sits immediate to the right of G, sits fifth to the left of D. 
F sits third to the right of H.
Thus, there are so many possibilities. Therefore, no definite arrangement can be established. 
So, statement I alone is not sufficient to answer the question. 
From statement II alone: 
Two persons sit between A and E. 
Neither A nor F is neighbour of B. Neither D nor F is neighbour of E.
Thus, there are so many possibilities. Therefore, no definite arrangement can be established. 
So, statement II alone is not sufficient to answer the question. 
From statements I and II together: 
Neither A nor F is neighbour of B. Two persons sit between A and E. 
| Case 1 | G | B | E |  |  | A | D |  | 
| Case 1a | G | B |  |  | E |  | D | A | 
| Case 1b | G | B |  |  | A |  | D | E | 
| Case 2 | A | G | B | E |  |  |  | D | 
| Case 2a |  | G | B | E |  |  | A | D | 
F sits third to the right of H.
Neither D nor F is neighbour of E. Thus, case 1a, case 1b, case 2 and case 2a are invalid. 
Therefore, we get:
So, only one person is sitting between E and H. 
So, both statements I and II together is sufficient to answer the question.