Final answer:
Peter the Great and Louis XIV both implemented absolute monarchies in their respective countries, strengthening their power and reducing the influence of the nobility without promoting democratic reforms or religious tolerance.
Step-by-step explanation:
The question explores how Peter the Great and Louis XIV were similar, and among the options, the correct one is that both implemented absolute monarchies in their respective countries, which is Option 2. Peter the Great centralized authority in Russia and pursued extensive reforms aimed at modernization and strengthening the state, while Louis XIV of France, also known as the 'Sun King', epitomized the divine-right monarchy. He strengthened the monarchy by centralizing power in his own hands, moving the royal court to Versailles, and enforcing absolute rule without any real checks on his authority.
Neither leader promoted democratic reforms or religious tolerance and cultural diversity as their governance was based on absolute authority, and both actively worked to reduce the power and influence of the nobility. In these ways, their ruling philosophies and actions demonstrate that they shared a common interest in strengthening their own power and implementing systems that ensured their control over the state.