The figure above shows the historic composition, as percentages, of

­ Photosynthesis is a process that uses atmospheric carbon dioxide to produce sugar and atmospheric oxygen. The most likely point for the first photosynthesis to have occurred is _____ years ago.

The solution depends on only the above diagram, which gives start/existence of various gases in atmosphere.
We are looking for the time when oxygen started being formed in atmosphere with availability of carbon dioxide in air too.

The start of oxygen(yellow portion) being formed is between 2 billion years ago and 3 billion years ago, almost 2.4 billion years ago.
Of course, we cannot be sure that the presence of oxygen is an irrefutable evidence that photo synthesis started then. Photo synthesis could have started anytime in last 2.4 billion years. But we are looking at most likely point and that could be the start of presence of atmospheric oxygen.

Well , just above the "2 billion " mark also we can see a big chunk of yellow ( indicating oxygen) and little bit green ( indicating CO2 ) .
Why not "2" then ?
I figured it out why it's not "2 billion years ago ". Because "2.4 billion years ago " is earlier than "2 billion years " ago. Since we are looking for "first photosynthesis to have occurred " , hence "2.4 billion years ago " will be more apt than "2 billion years" ago.chetan2u MartyMurray

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