Final answer:
The Monroe Doctrine's statement that the U.S. would not intervene with existing western hemisphere colonies reassured the governments of these small territories that their political status would be respected and protected from further European colonial expansions.
Step-by-step explanation:
The importance of the statement "the United States wouldn't intervene with existing western hemisphere colonies" within the Monroe Doctrine is best explained by Option 4: In most cases, territories wanted to keep independence, and colonies were already ruled by a foreign country. For the government of a small colony near the United States, this aspect of the Monroe Doctrine would be crucial as it implied that the U.S. would not meddle with the affairs of existing colonies, thereby respecting their current political status and possibly preventing further European colonial expansions or interventions in the Western Hemisphere.
This stance was particularly relevant at a time when the Latin American colonies were seeking independence from European powers and navigating the complexities of becoming stable, self-governing nations. As such, the Monroe Doctrine contributed to the idea that Latin America was free and independent from foreign intervention, which was particularly significant for the smaller, more vulnerable territories and newly independent states.