How did the allies defeat general rommels forces?

The Allies, under the command of British General Bernard Law Montgomery, defeated the forces of General Rommel at the Battle of El Alamein in 1942.  Rommel had been dominant in the deserts of North Africa until 1942, but as Rommel's Afrika Korps was preparing to strike at the British at El Alamein in the spring of 1942, their strength was depleted.  At that point Rommel had just 125 operational tanks, and Hitler did not grant reinforcements, because he was focused on the battlefront with Stalin and the USSR.  The British used the hiatus in the fighting to reinforce their forces of tanks, troops, artillery and ammunition in Egypt (including Sherman tanks from the USA), and thus were able to overcome Rommel's forces when the El Alamein battle was waged in the fall of 1942.

Upon the fall of rome, europe ceased being influenced by the cultures of the mediterranean coast and was more influenced by germanic tribal confederations that had already taken over vast swathes of roman territory, although the influence of rome on the former empire was very strong in legal