Final answer:
Napoleon Bonaparte drove royalists out of the National Convention in 1795 by using a decisive and violent method known as a 'whiff of grapeshot,' firing cannons into the crowd, effectively ending the counterrevolutionary threat.
Step-by-step explanation:
Napoleon Bonaparte, a figure closely aligned with the French Revolution, swiftly gained notoriety when he suppressed a royalist insurrection at the National Convention in 1795. The method Napoleon employed to drive the royalists out of the National Convention is best captured by option (a): he ordered a 'whiff of grapeshot' into the crowd, which was a mass of small metal balls fired from cannons. This decisive and brutal act not only quelled the counterrevolutionary activity but also cemented Napoleon's reputation as a hero and savior of the revolutionary government. This pivotal moment led to his subsequent appointment as the commander of the French army in Italy and a military advisement role with the Directory, setting him on the path to establishing his dominance in French politics and military affairs.