Final answer:
Austria and Prussia helped Louis XVI protect the French monarchy, aiming to restore the traditional balance of power in Europe and maintain the legitimacy of European monarchs against the spread of revolutionary ideals.
Step-by-step explanation:
The assistance that Austria and Prussia provided to Louis XVI was not to promote democracy, gain control of French territories, or support the French Revolution. Instead, it was to protect the French monarchy. The explanation for this lies in the broader context of European politics at the time.
Monarchs like Metternich of Austria wanted to restore the balance of power in Europe after the upheaval caused by the French Revolution and Napoleon's conquests. The aim was to ensure that no single country could dominate the continent and that the traditional monarchal order could be maintained, representing a conservative reaction against the revolutionary ideologies that threatened the existing social and political order.
After the execution of Louis XVI, the forces of the revolution in France not only faced internal strife (between groups like the Girondins and Jacobins) but also external threats. Austria and Prussia, along with other monarchies, viewed this political disturbance as an existential threat to their own sovereignty.
As they sought to restore the legitimacy of European monarchs, they supported Louis XVI against the revolutionaries in hopes of preventing the spread of revolutionary ideals and preserving their own autocratic power structures.