Final answer:
European absolute monarchs supported King Louis XVI to maintain similar dynastic and political interests and to suppress the spread of democratic and revolutionary ideas that could challenge their power.
Step-by-step explanation:
The absolute monarchs of Europe would have supported King Louis XVI because they typically upheld similar dynastic and political interests. Monarchs like Louis XVI, who ruled with absolute power, exemplified the belief in divine right and the centralized control of the state.
Monarchs were also motivated by a shared interest in suppressing democratic and revolutionary sentiments that were gaining ground. The success of the American Revolution inspired those in France who opposed absolute monarchy and aristocratic privilege, which constituted a threat to the reigning monarchs in Europe.