From statement I alone -
Statement I: C sits second to the left of F. Two persons sit between B and G, who sits immediate left of D. Neither B nor D sits adjacent to E. A sits third to the right of E. F does not sits adjacent to B.
Two persons sit between B and G, who sits immediate left of D.

A sits third to the right of E.
Neither B nor D sits adjacent to E.

C sits second to the left of F.
F does not sit adjacent to B.

Now, only H is remaining.

Three persons sit between H and D when counted from the left of D.
From statement II alone -
Statement II: Two persons sit between G and B. E does not sit adjacent to A. Three persons sit between A and F, who sits second to the left of G. C sits immediate left of H but not adjacent to A. Only one person sits between D and E.
Three persons sit between A and F, who sits second to the left of G.

Two persons sit between G and B.

C sits immediate left of H but not adjacent to A.

Only one person sits between D and E.
E does not sit adjacent to A.

Three persons sit between H and D when counted from the left of D.
Hence, the data either in statement I alone or in statement II alone is sufficient to answer the question.