There are no immediately obvious connections between the two events, except that both events are being widely deconstructed, misrepresented, or forgotten.
June 6th, 1944 was the day when Allied forces, composed of American, British, Canadian and Free French, landed on the Normandy beaches starting a major battle for the liberation of Europe from Nazi tyranny. America lost more of its young soldiers in battle on that first day than have been lost in the many years of struggle against al-quaeda and other terror forces in Iraq and Afghanistan, for one comparison. The Brits and Canadians lost even more. For those who weren't taught anything about this in their history classes, or for the younger generation which seems more enamored with DVDs than books, I would recommend "Saving Private Ryan" or "The Longest Day" for a glimpse into the what their American (and Canadian and British) ancestors were up against, and what they did, to prevent the Hitler fanatics from grabbing even more of the world than merely Europe and North Africa. American ships were being regularly torpedoed off New York and Los Angeles harbors in those days, long before war was declared against the USA, long before Pearl Harbor was attacked, by Japanese and German U-Boats. The American military machine hardly existed only 20 years earlier, having been created out of nothing basically by FDR, who mobilized American industry to the task. All the people who today want to denounce American influence around the world, or how many American soldiers are stationed overseas at critical geographical locations, would do well to remember the totalitarian condition of the world prior to the Normandy Invasion, or VE and VJ Day. And if you don't know what those terms mean, then really you do need to study the history.
June 6th, 1968 was also the day Robert Kennedy was assassinated. A decent fellow and promising candidate for President, he was shot dead by a Muslim terrorist, one of the very many Islamic atrocities which occurred in the 20th Century, long before the word "Islamofascist" or "Jihad Terrorist" was coined for popular understandings after 9-11-2001. But in fact he was gunned down by a Muslim fanatic for his strong support for Israel, for his dislike of the totalitarian Arabist and Islamic wars and agendas he personally eye-witnessed, especially during his trips to Israel in 1948. You can read Bobby Kennedy's views in his own words at the link below, and contrast them to the views and beliefs of those who abuse his name as justification for every kind of incredibly naive or hard-left program. As a young journalist for the Boston Post, he got it more accurate and correct than most, including the NY Times, whose reporters have a chronic habit of fabricating stuff to support the COMINTERN, or to denigrate the Jews of Israel, or their fellow Americans. I remember how, when Bobby Kennedy was killed, all my liberal-left friends automatically collapsed into terrible rants about CIA conspiracies, or vented hatred at the Republicans. I was ignorant also, but was wise enough to keep my mouth shut about things I did not know. But in fact, as I learned later, it was the Muslim fanatics who killed Bobby Kennedy, while his brother, most people will forget, was killed by a dedicated Communist assassin.
Historical accuracy is important, if only to recognize similar patterns emerging, and to hence avoid repeating the bloody errors of the past.
On the 40th Anniversary of His Assassination:
Robert Kennedy's 1948 Reports from Palestine