You didn't attach the map you were shown, but I can tell you what that map would look like.
Israel had gained control of several sections of territory which they had not previously controlled. In the south, Israel now held control of the Gaza Strip and the Sinai Peninsula (which had been held by Egypt). Along the Jordan River, Israel now controlled the region known as the West Bank (which was a region where Palestinians lived). In the north Israel had taken the Golan Heights away from the control of Syria.
In negotiations after the war, there were thoughts of returning land for peace, but that really only has happened in the case of Israel's relationship with Egypt. (Israel and Egypt signed a lasting peace agreement in 1979.)
The British had tons of internal and domestic problems to face their own, so basically from the beginning (early 1600's) they entered into a period of salutary neglect (where they didn't enforce their own laws)
