Birthday of Carl Gustaf Emil Mannerheim & Flag Day celebration of the Finnish Defence Forces

Namibian Armed Forces Day on June 3;

Mabo Day in Australia on June 3 (It commemorates Eddie Koiki Mabo (c. 29 June 1936–21 January 1992) a Torres Strait Islander whose campaign for Indigenous land rights led to a landmark decision of the High Court of Australia that, on 3 June 1992, overturned the legal fiction of terra nullius which had characterised Australian law with regards to land and title since the voyage of James Cook in 1770);

Tiananmen Square Protests of 1989 Memorial Day on June 4 (International);

June 4th revolution in Ghana on June 4 (1979);

Estonia Flag Day on June 4;

Canadian Forces Day on June 6 (celebrated on the first Sunday in June);

Normandy landings of the Allied Expeditionary Forces on June 6 (D-Day), a.k.a. Operation Neptune, part of Operation Overlord (1944);