With the caveat that I always try and avoid secondary sources if I want reliable info, the following is taken from Farndale's "The Years of Defeat 1939-41"
Pg 119 - 106 (Lancs Yeo) Regt part of 1 Cav Div, horsed, arrived Palestine (Haifa) 20 Feb 41. Soon began to mechanise (those familiar with Ahrenfeld's history of psychiatry in the Brit Army will know how difficult it was to train donkey wallopers onto vehicles). Sep 1940 all 3 regts (104, 106, 107) moved to W Desert to prep posns in Baggush Box (date inconsistent with next mention).
Pg 121 - May 1940, 106 Fd Regt RHA with 7 Armd Div. Mersa Matruh area.
Pg 126 - Sep 1940, Wavell moved div tps of 1 Cav Div (104, 106, 107 Regts RHA) from Palestine into Egypt, all mechansied and each with 8 x 18-pr & 8 x 4.5-in How (ie still on cav div org of 2 btys per regt). Arrive Baggush end Sep.
Pg 136 - 3 Jan 41, 6 Aust Div attack on Bardia, forces included 106 ATk Regt RHA.
Pg 140 - 2 tps 106 ATk Regt with 4 Armd Bde (could be interpreted as only 2 tps per bty). Refs to btys as 1/106 and 2/106.
Pg 141 - Colm of 2RB, sqns 11H & KDG reach Antelat. RB coys had sect of 37mm from 106 ATk RHA. Remainder of 4 Armd Bde Gp included rest of 106 RHA.
Pg 143 - from 7 Armd Div War Diary 7 Jan "the guns of 106 Regt RHA gradually knocked out the en tks, the last one only a stone's throw from the officers mess truck". 106 Regt claimed 27 en tks dest.
Pg 170 - In Feb 1941 HQ 2 HAA Regt arrived (in Piraeus, Greece), . . . next came 106 LAA Regt RHA, commanded by Lt Col Hely, hastily converted from its former anti-tank role and equipped with 36 x 20mm Breda guns captured from the Italians.
Pg 171 - By 9 Apr GE had captured Salonika . . . 19 Aust Inf Bde with 2 Regt RHA, 106 ATk Regt RHA, 64 Med Regt, 2/3 Aust Fd regt and 2/1 Aust ATk Regt . . . rushed to hold the pass at Veve.
Pg 174 - (date from context 20-26 Apr) . . . 20 x 20 mm Bredas of 106 LAA Regt RHA left to cover the withdrawal.
Pg 176 - (29 Apr?) . . . 106 LAA Regt RHA destroyed its Breda guns wile savage air attacks developed on the Argos airfields. This splendid regt had suffered severely and on its withdrawal to Crete was to fight as infantry at Suda bay under its intrepid commander Tim Hely. In this battle after all it had done in the desert and in greece it was decimated and had to be disbanded; the end of a very gallant regt indeed.
Pg 190 - June 1941, ORBAT for OP BATTLEAXE, 106 Regt RHA - 7 Armd Div LAA Regt.
Pg 323 - 106 Regt RHA - Lancs Yeo. LAA Regt RHA Mar 41. Disbanded Jul 41.
Pg 328 - 106 ATk Regt - formed Jun 4 in ME disbanded Mar 44.
Pg 338 - 106 LAA Regt - formed from 106 Lancs Yeo RHA Mar 41.
Horner "The Gunners - A History of Australian Artillery"
Pg 248 - ORBAT for Greece - Force Tps - 106 LAA Regt RA
Also 102 ATk Regt RHA with 1 Armd Bde Gp. Horner makes no other ref to any 106 regt.
Farndale pg 172 refers to "Lt Tripper's 2-prs of 104 Regt RHA", however I think it should be 102 ATk Regt formed Mar 41 from 102 LAA/ATk Regt (NH). I think the pg 171 ref to 106 should be 102.
Pg Pg 328 'no record of 104 ATk Regt being formed'
I trust everyone is now well and truly confused.