Back to the Western Desert in June 1942

The events in Syria in early 1942 seemed like a side-show. The real action was in the Far East and in the Western Desert. The Far East had a significant effect on the situation in the Mediterranean and Middle East. Formations from the Middle East were sent to the Far East, such as the 6th and 7th Australian Divisions. From the beginning of 1942 up to April, "180 bombers and 330 fighters" were transferred to the Far East.
The facts were, for the British, were that despite winning the Crusader Battle and breaking the siege of Tobruk, they were unable to exploit that success. The reasons were the commanders that they had were inferior as were the methods that they used for employing tanks and artillery. General Auchinleck's personal involvement to some extent could overcome those issues, but they were not really solved until Bernard Law Montgomery arrived in the Middle East to command the Eighth Army. The effort required to supply and arm Malta was also a drain on resources. This primarily affected the navy and air force.
During the middle of December 1941, the Axis forces pulled back from Gazala to Agedabia. This meant that the British were able to move into Benghazi "on Christmas eve". The Guards brigade (presumably the 22nd Guards Brigade) had moved forward to "make contact" with the enemy forces by 22 December 1941. The British 1st Armoured Division moved to the west to be close to the enemy. The Axis forces responded by pulling back to Tripolitania. Early in January 1942, the small groups of Germans "at Bardia, Salum and Halfaya" were captured.
The Italian navy was able to push a convoy through to Tripoli (Libya) on 5 January 1942. The convoy brought armored vehicles and supplies that allowed Rommel to quickly attack the British. Sadly, the British were caught by surprise. Rommel was strong enough to be able to push the British forces back to the Gazala line. Gazala was reached on 6 February 1942. This is based on the account in Vol.III of the Australian Official History.