Final answer:
The most clear fact showing the difficulty in defending the Roman Empire against invasion is the weakened Roman military and leadership, the misjudgment of territorial losses, and the greater barbarian threat, which all contributed to the empire's eventual fall.
Step-by-step explanation:
The fact that most clearly shows the difficulty in defending the Roman Empire against invasion is the eventual disintegration of Roman power due to a combination of factors. These factors included the under-funded and under-manned Roman armies in the west, the growing number and improved organization of barbarian groups, and the failure to effectively respond to territorial losses, indicating the decline in military efficacy and leadership.
Large-scale invasions, such as when barbarians crossed the frozen Rhine in 406 CE, further exemplify the Roman military's weakened state. Moreover, the Roman leadership didn't consider the persistent losses of territory to barbarians as pivotal, signifying a misunderstanding of the empire's declining strength. The shift in focus towards the east and away from the increasingly vulnerable western territories accelerated the disintegration, resulting in the multiple sackings of Rome and loss of western territories over the centuries.