This period precedes the British involvement against the German Africa Corps in Egypt.
Italy was the initial aggressor, putting 250,000 troops up against 100,000 British men in an attempt to tie down the entire English Middle East compliment, prior to the planned invasion of Greece by the Italians from bases in Albania.
The Italian Tenth Army invaded Egypt 13 Sep 40,resulting in a general retreat by the British against such overwhelming strength. This enncouraged the Italians to erect a series of five fortified camps between Sofafi and the Mediterranian, some 60 miles inside Egypt.
After a period of several months, General Sir Archibold Wavell, Commander-in-Chief in the Middle East from July-1939, ordered his Western Desert Force to counterattack. This started 9 Dec 39.
The 6th Australian Division captured Benghazi 6 Feb 40, which was to prove to be the only Allied victory in the Middle East until the glorious victory at the Battle of El Alamein, 23 Oct / 5 Nov 42.
Other elements of the British Eighth Army included the 7th Armored Division and the 4th Indian Infantry Division.
The Italians were overwhelmed by the British manuevers, with the fortified ports of Bardia and Tobruck ,Libya, falling easily.
The British cut off the escape route to Beda Fomm, and when the Italians gave up, they lost 130,000 men as prisoners, 845 guns and 380 tanks. Britain had lost less than 2,000 men, killed, wounded and missing.
The Italians surrendered to Wavell's forces 6 Apr 40, followed by the almost immediate arrival of the Africa Corps in Egypt, 14 Apr 40.
The rest became history, with the British victory at El Alamein in 1942. Of course it wasn't over, for the great battle for Tunisia was still to come.
All of which is to say that your grand father was in Egypt to help put down the Italians in their master plan, and to face and defeat the Germans in their massive efforts.