who were the allied forces of the operation?
22nd Guards Brigade and elements of the 7th Armoured Division.
Operation Brevity
Operation Brevity would be carried out by the 22nd Guards Brigade and elements of the 7th Armoured Division. 
what was operation brevity? A limited offensive conducted in mid-May 1941. did it operate during any war? Second World War. who commanded the operation then? General Archibald Wavell where is he from? UNANSWERABLE
wiki:14151265
Operation Brevity [SEP] Allied force
Operation Brevity would be carried out by the 22nd Guards Brigade and elements of the 7th Armoured Division. Its armoured component consisted of 29 cruiser tanks of the 2nd Royal Tank Regiment (2RTR) and 24 infantry tanks of the 4th Royal Tank Regiment (4RTR). The Royal Air Force (RAF) allocated all available fighters and a small force of bombers to the operation. Brigadier William Gott—in command of all Allied front-line forces since the retreat—was to lead the operation in the field, and his plan was to advance in three parallel columns. On the desert flank to the south, the 7th Armoured Brigade group was to move from Bir el Khireigat to Sidi Azeiz destroying any opposition encountered en route.