August 1942, Japan and Argentina both conducted their invasions of both the Philippines and Falklands, in the Philippines, US General Douglas MacArthur and his troops were caught off guard and were retreating and began digging their feet in Manilla with tanks and outdated aircrafts waiting for the Japanese.
On paper the US army outnumbered the Japanese with 151,000 US and Filipino soldiers and 108 tanks compared to the enemy 129,500 and 90 tanks, however the US forces were comprised of experienced and inexperienced soldiers, national guards, and Filipino constabulary policeman compared to the battle tested and experienced Japanese soldiers, veterans of the Indochina, Indonesian, and Malaya campaigns.
The final nail in the coffin was the superiority in airplanes the Japanese had: 541 Zeros and bombers to the US 277 planes.

Gen. Douglas MacArthur

The beginning of the invasion
The Japanese attacked from both North at Luzon and Bataan while also, later on, from the south from Indonesia,l. The lightening attack took the US soldiers by surprised, made worst with enemy planes wiping out the American planes.
The first battle in the invasion was the Battle of Bataan on August 7, in which Gen. MacArthur was defending Bataan and Manilla Bay in a fighting retreat and despite being outnumbered, outgunned, and unsupported the American and Filipino soldiers managed to delay the Japanese invasion for a astounding three months but it finally came to an end on November 2, when the Japanese from Indonesia invaded, capturing the southern Islands. The battle was lost and MacArthur decided to retreat to Manilla were he was determined to make his last stand.

Japanese tank column on the move.
The United States of America was absolutely outraged and decided that being isolated was no longer a option: on August 15, President Franklin Roosevelt asked Congress for a declaration of war against the Empire of Japan, Congress voted unanimously and now the United States was at war against Japan. Immediately National France, the Union of Britain, and the Soviet Union declared war on the United States, bringing her into the wider side of the Weltkrieg.
The Allies, especially Mexico, accepted the United States with opened arms with Prime Minister Cárdenas being the first Mexican leader to visit the White House and meet with the President. Both agreed that Europe was first and after all of the Axis powers in Europe were defeated, then they can focus on the Soviet Union and Japan.

President Roosevelt
Immediately a general mobilization was called and plans were being drawn up to help The Danubian Empire, Kingdom of the Two Sicilies, the MEF, and the Ottoman Empire against the Kingdom of Sardinia and Greece the two of which were as described by Prime Minister Winston Churchill as "The weak underbelly of the Axis."

Uncle Sam
In Argentina, the surviving Destroyers, cruisers, and light cruisers launched Operación San Martín: the invasion of the Falklands. The Argentine force was formidable; it included 30,000 soldiers, 20 Nahuel tanks, and 14 bombers all under command of Lieutenant General Eduardo Lonardi. The Canadian forces on the Falklands were not standing idly by, they were warned in advanced by the Marina Imperial but Rule Britannia was no more and the Commonwealth Navy was stretched to the absolute limit, with one half helping the Allies in India and the other half patrolling the northern Atlantic to make sure the Union of Britain Navy didn't make a break out, so they were only able to send two Battleships:
HMS Nelson and
Rodney as protection against any Argentine fleet along with a additional 5,000 Commonwealth troops.

Gen. Eduardo Lonardi

Argentine soldiers (note the helmets)
Nelson and Rodney
The Argentine Navy was in a not bad, but still in a sordid state: after major repairs that took the duration of June and July the
Belgrano was fully repaired, pre-battle of Buenos Aires, and was upgraded with a 200 mm main gun and major construction was also made on the remaining destroyers and cruisers and after months and planning the operation was carried out and the plan was to land in Stanley and proceed forward from the East to the Western half of the islands. Operación San Martín began on August 7 with the Argentine Armada completely bypassing the Commonwealth Battleships, who were stationed on the Western half in the Weddell settlement were they assumed the Argentines would attack. They were wrong.
The Argentine attack commenced at 9:00 a.m. when the
Belgrano fired onto the harbor and the smaller ships began landing troops and tanks, while the ANZAC forces were being pinned down by the shells coming down on them. By 9:30 the full Argentine force were on the port and were fighting their way towards the city, realizing they were completely outnumbered and outgunned General Claude Auchinleck, decided it was better to retreat to Goose Green than be annihilated in a war of attrition.

Claude "The Auk" Auchinleck
The Argentine forces captured the city and declared that the reconquista of the Malvinas was nearly complete. However two days later, a major wrench was thrown at the gears: On August 11 the
Belgrano was on a patrol along with two destroyers at the Choiseul Sound passage where they encountered the
Nelson and
Rodney.
The Battle of Choiseul Sound began with duel between
Nelson and
Belgrano while the
Rodney took on the destroyers. Immediately it became clear on who had the advantage; even with the upgrades
Belgrano neither had guns nor armour to inflict any damage on
Nelson and nor could she take the absolute pounding the
Nelson was dealing her and after 20 minutes
Belgrano raised the white flag surrendering while the two destroyers were absolutely thrashed by
Rodney with one seriously damaged and the other sinking. The battle slowed the invasion to a halt and immediately Argentina began looking towards Chile for ships to go toe to toe with the Commonwealth.
Meanwhile in the Balkans...