Well in the 6 day war only a token Iraqi force was available and it was under Jordanian command. When Jordanian agreed to give up the west Bank and Jerusalem without a shot the Iraqi commander refused and fought a losing battle which was the only action in that region. In Syria the Iraqi forces reached after the cease fire.
In the 73 war on the other hand the Iraqis were the only undefeated Arab force and the only one that won all its battles. The repulsed an Israeli armourred offensive south of the Golan and liberated part of the Syrian territory there. They also helped repulse the Israelis on the Damascus road and advanced several Kms. The Iraqis had a 30k strong corps and another corps on the way when the cease fire was accepted by the Syrians despite Iraqi objections (this story alone is too long for this thread and it was one of the causes of the rift between Syrian and Iraqi Baath parties later).
Al-Jassas