Final answer:
The war between Austria, Prussia, and France in 1792 was primarily ignited by the monarchies' attempts to suppress the spread of revolutionary ideas emanating from France and to restore the power of King Louis XVI.
Step-by-step explanation:
The reasons Austria and Prussia went to war against France in 1792 revolve around the complex interplay of political dynamics in Europe following the French Revolution. Austria, Prussia, and other monarchies were concerned about the rise of radical groups within France, such as the Girondins and Jacobins, and the momentum towards ending monarchy and spreading revolutionary ideas. In an effort to restore the power of King Louis XVI, these countries plotted against France, leading to France's declaration of war on Austria in 1792.
Furthermore, France's revolutionary effort sought to spread its ideas across Europe, which threatened the existing social and political order and prompted a defensive response from Austria and Prussia. The threat of these radical changes spilling over into their own territories was a major factor in the decision of Austria and Prussia to go to war against France, in hopes of curbing the French Revolution's influence.