Final answer:
The Archean Eon is the correct answer as it was during this time that early anaerobic life forms absorbed nutrients through osmosis in an anoxic atmosphere, prior to the accumulation of oxygen produced by the advent of photosynthesis.
Step-by-step explanation:
The statement that organisms gained nutrients through osmosis likely refers to the early anoxic conditions of Earth where the earliest life forms were anaerobic and could not utilize molecular oxygen. This anaerobic environment was prevalent during the Archean Eon, which spans from about 4 to 2.5 billion years ago. During this eon, the atmosphere was devoid of oxygen, and it was only later, with the emergence of cyanobacteria and the onset of photosynthesis, that molecular oxygen started accumulating in the atmosphere. This process of photosynthesis likely began between 3.5 and 2.5 billion years ago, within the Archean Eon, thus making it the correct answer, B) Archean Eon.