During origin of life, eukaryotes originated about ................ million years back.

Chemosynthesis of self replicating nucleic acids and proteins followed by aggregation of proteins around nucleic acid resulted in origin of first life form, around 2000 million years back. Thus, the first life forms were nucleoproteins that lack any definite nucleus i.e. they were prokaryotic chemoheterotrophic organisms. This makes option B incorrect. 

Compartmentalization of prokaryotic cells by infolding of plasmalemma resulted in formation of intracellular membrane bound organelles. Endosymbiosis of colorless and blue green cyanobacterium into another bacterium gave rise to mitochondria and chloroplast respectively. Presence of mitochondria allowed oxygenic respiration which was favoured over anaerobic oxidation of organic compounds owing to its high energy yield. All of these events caused evolution of eukaryotic cells from prokaryotic organisms around 1500 million years ago. This makes option C correct. 

The period of 6 million years ago is marked by appearance of first human like organisms as a result of split between hominids and chimps. Hominids differ from apes in living on land, not on trees, and walking on toes. This makes option D incorrect. 

Therefore, the correct answer is option C.