Final answer:
The British government stationed soldiers in the colonies for protection and to enforce taxes and policies, justified by mercantilism. Colonists disapproved due to the burden of support and infringement of political rights.
Step-by-step explanation:
The British government justified the stationing of 10,000 British soldiers in the colonies primarily for protection against external threats and to enforce policies and taxes under the mercantilist system. They maintained troops in North America to police the frontier, regulate colonial trade, and ensure tax collection. The costs associated with maintaining the army led to new taxes on the colonists or to more aggressive enforcement of existing ones. The colonists disapproved of these measures for several reasons. The presence of soldiers infringed upon their perceived political rights, such as the right to protest policies they disagreed with. They also disapproved of the quartering and maintaining of soldiers, which included providing lodging and food, as dictated by the Quartering Act of 1765. This was burdensome and compounded the distrust towards a standing army during peacetime, a sentiment with historical roots since the reign of James II.