What is an example describing a specific situation where the principle of checks and balances could be used for the good of the people?

The president can veto any bill passed by congress, But a two thirds in congress can override the veto.

Explanation:

the house of representatives has sole power of impeachment, but the senate has all power to try any impeachment or decisions made by the president.

I believe it is both Greek and Rome, but more of Greek
 Greek is mentioned in relation to democracy, especially the weaknesses of direct democracy, where citizens would congregate at the mount to air their views and elect the candidate of their choice. The candidate who had hired the most talented shouters often won. The limitation of mob type of democracy informed the rationale behind the electoral college.

Rome is mentioned in relation to the course of imperialism on national cohesion and stability, as well as the capture of a good democratic course by totalitarian regimes.