Final answer:
Between 1641 and 1679, New Hampshire merged with the Massachusetts Bay Colony. They functioned under one administration due to the substantial influx of Puritans who established the Massachusetts Bay Colony.
Step-by-step explanation:
From 1641 to 1679, the colony that New Hampshire merged with was the Massachusetts Bay Colony (option A). During this period, the two colonies worked together and were effectively under one administration due to the larger exodus of Puritans that established the Massachusetts Bay Colony in the 1630s. These Puritans sought to create a reformed Protestantism, a 'city upon a hill', which was the religious orientation of the New England settlement at the time.
However, in 1686, all the New England colonies, including Massachusetts and New Hampshire, were joined together into a single unit known as the Dominion of New England under the reign of James II.
Learn more about New Hampshire and Massachusetts Bay Colony