Which of the following was an achievement of Charlemagne?

A. becoming mayor of the palace
B. allowing the Lombards to spread Christianity
C. unifying western Europe under a single ruler
D. preventing Muslims from conquering western Europe

The correct answer is C. unifying western Europe under a single ruler.

To find the answer, we need to analyze each option and determine which one aligns with Charlemagne's achievements.

Option A, becoming mayor of the palace, is incorrect. Charlemagne did not achieve this. The title of mayor of the palace was actually held by his father, Pepin the Short.

Option B, allowing the Lombards to spread Christianity, is also incorrect. Charlemagne campaigned against the Lombards in Italy and defeated them, rather than allowing them to spread Christianity.

Option D, preventing Muslims from conquering western Europe, is also incorrect. While Charlemagne did engage in military campaigns against Muslim forces in Spain, he did not prevent them from conquering Western Europe entirely.

This leaves us with option C, unifying western Europe under a single ruler, which is the correct answer. Charlemagne's most significant achievement was his successful effort to unite several Germanic tribes and various other regions under his rule, creating the Carolingian Empire. Through his military campaigns and diplomatic alliances, Charlemagne expanded his empire and brought a large portion of Western Europe under his control.