The correct answer is option 'B', the Neolithic age.

Explanation:
The Neolithic Age, also known as the New Stone Age, was a period in human history that marked the transition from hunting and gathering to agriculture and the development of settled communities. It is during this period that early man started manufacturing earthen jars.

Here is a breakdown of the answer:

1. Neolithic Age:
- The Neolithic Age is characterized by the development of agriculture, domestication of animals, and the establishment of settled communities.
- It is estimated to have started around 10,000 BCE and lasted until around 4,000 BCE.
- During this period, humans transitioned from a nomadic lifestyle to a settled one, relying on farming and animal husbandry for sustenance.

2. Manufacturing Earthen Jars:
- The development of agriculture in the Neolithic Age led to the need for storage vessels to store surplus crops.
- Early humans began to manufacture earthen jars to store and preserve food and other valuable commodities.
- These jars were made by shaping clay into specific forms and then firing them in kilns to harden them.

3. Importance of Earthen Jars:
- Earthen jars were crucial for the storage and preservation of food and water.
- They provided a means to store surplus crops and reduce dependence on immediate consumption.
- The use of earthen jars allowed for the development of trade and economic systems, as excess goods could be stored and exchanged.

4. Mesolithic Age and Paleolithic Age:
- The Mesolithic Age and Paleolithic Age were earlier periods in human history.
- The Paleolithic Age, also known as the Old Stone Age, was characterized by the use of stone tools and a hunter-gatherer lifestyle.
- The Mesolithic Age followed the Paleolithic Age and saw the development of more advanced tools and the beginning of the domestication of animals.
- However, the manufacturing of earthen jars did not occur during these periods.

In conclusion, it was during the Neolithic Age that early humans started manufacturing earthen jars as a result of the development of agriculture and settled communities.