Answer: D. Their rulers claimed power by virtue of protecting Dar al-Islam from European invasion
Explanation:
The images described are not attached however based on a similar question that you posted, I can infer that the empires being described are two of the three Muslim empires of the Ottomans, Mughals or Safavids which came to prominence around the same time.
These empires, especially the Ottomans and the Mughals, used gunpowder technology to capture large areas of land. They claimed they were doing so to ensure that they spread the doctrines of Islam and to protect Islamic lands from European invasion.