Which one provides direct and solid evidence in favour of organic evolution through ages?

The correct option is D Palaeontology/fossils
Atavism :
Atavism is the sudden reappearance of some ancestral characters.It does not provide direct evidence for organic evolution.

Palaeontology/fossils :
Palaeontology is the study of fossils.Fossils are the impressions or remains of the hard parts of the organisms which got buried in the strata of the earth in the past.
Comparative study of anatomical features of a detailed fossil record provides direct and solid evidence for the evolutionary progress on earth over millions of years.

Vestigial organs :
Vestigial organs are the remnants of organs which were functional in the ancestors. For instance, nictitating membrane in humans are vestigial organs and do not provide direct evidence for organic evolution.

Galapagos island fauna :
The various fauna of Galapagos island helped Darwin support his theory of natural selection.

Final answer:
(B) Palaeontology/fossils