The answer it’s number 4 “implied power”

The word "New Right" appeared during the 1964 presidential campaign of Barry Goldwater to designate "the emergence, in response to liberalism (in the American sense of the term [i.e. social liberalism]), of an uninhibited right: ultraconservative, imbued with religious values, openly populist, anti-egalitarian,
Because for them they wanted to reunite and conquer the other country
Answer: Nations of Latin America won independence
Explanation:
As Creoles and Mestizos became discontented with Spanish rule, they began to demand more self-governance from the Spanish which would eventually boil over to them asking for independence.
This was made easier when Napoleon invaded Spain during the Napoleonic wars and severely weakened Spain's power to hold onto its colonies. Revolutions in North America such as the American Revolution spurred some colonies to seek independence such as Haiti from France which went through its own Revolution as well.
These three factors allowed nations in Latin America to seek their independence and led to many getting it.