The correct answer is option 2: American war of independence.

"No Taxation without Representation" was a popular slogan used by American colonists during the American war of independence, which took place between 1775 and 1783. This slogan reflected the colonists` dissatisfaction with being taxed by the British government without having any representation or say in the decisions that affected them. The British government imposed various taxes on the American colonies, such as the Sugar Act, Stamp Act, and Townshend Acts, which were viewed by the colonists as unfair and a violation of their rights.

The slogan became a rallying cry for the colonists, expressing their desire for self-governance and representation in the decision-making process. It played a significant role in uniting the colonists in their resistance against British rule and fueling the spirit of revolution. Ultimately, the American war of independence led to the formation of the United States of America as an independent nation, free from British control.

Therefore, the correct answer is option 2: American war of independence.