There were not six nations involved in the D-Day landings. There were, instead, three nations that were involved in major ways and a total of twelve that were involved in one way or another.
The three countries that were involved in major ways in the D-Day landings were the United States, Britain, and Canada. US troops landed on Utah and Omaha beaches. The British landed (with some French) on Sword and Gold. The Canadians landed on Juno.
Other countries that were involved in the invasion included Australia, Belgium, Czechoslovakia, France, Greece, the Netherlands, New Zealand, Norway and Poland.