Final answer:
The Mongolian Kahn’s difficulty with bringing Vietnam under the pax Mongolica can be attributed to geographical challenges, cultural resistance, and military strategies, including the Vietnamese use of guerrilla warfare and their deep resentment of foreign rule.
Step-by-step explanation:
The difficulty with bringing Vietnam under the pax Mongolica can be best explained by geographical challenges, cultural resistance, and military strategies. The expansive river systems and the terrain itself in southern China and Vietnam posed significant obstacles to the Mongols' traditional cavalry-based military tactics and their ability to exercise control. Additionally, the Vietnamese employed guerilla warfare tactics, taking advantage of their knowledge of the local terrain. Cultural resistance also played a vital role as the notion of foreign rule was deeply resented by the population. As for their attempts in South Asia, specifically the Delhi Sultanate, the Mongol khanate weakened itself through several failed attempts, in part due to the strong military strategies of the sultanate's forces and possibly also the harsh climatic conditions and long supply lines that would have affected the Mongol armies.