What territories did Israel gain from the Arab-Israeli conflict?

Answer 1

At one point, Israel controlled all of the Palestinian regions set apart from the nation, the Sinai Peninsula all the way to the Suez Canal, and Syria's Golan Heights. They eventually conceded some of those territories for peace, pursuant to UN Resolution 242.

Answer 2

The question as phrased makes an implicit assumption which is not true, namely that the Palestinians were part of the Six-Day War. While it is true that lands that Palestinians claim were involved in the war, the PLO and other Palestinian Militant Organizations either did not exist in 1967 or did not directly contribute to the fighting. Another misconception is that Israel acquired only four distinct regions in the aftermath of the Six-Day War. When the regions are properly counted, Israel acquired 5-6 regions as a result of the War. (The difference is between whether Jerusalem is considered part of the West Bank.)

Territories

As for the territories acquired, they were (in order of size): the Sinai Peninsula (from Egypt 1967-1982), the West Bank (from Jordan 1967-Present, some parts devolved to the Palestinian Authority), the Golan Heights (from Syria 1967-Present), the Gaza Strip (from Egypt 1967-2005 to the Palestinian Authority), the Eastern Bank of the Sea of Galilee (from Syria 1967-Present), and East Jerusalem (from Jordan 1967-Present).

To see the list of territories for which Israeli occupation was legitimated subject to a future peace treaty according to UN Resolution 242, see the list below:

East Jerusalem: Considered by many Israelis to be the greatest success of winning the Six-Day War, Israel was able to unite the city of West New Jerusalem with the Old City and East New Jerusalem to create a united municipality and capital (although unrecognized internationally as such). Of the territories here considered it is the smallest and most controversial as Palestinians want East Jerusalem and the Old City to be part of their eventual capital city.

West Bank: From 1949-1967, this area was a province of Jordan and included all areas within the Mandate of British Palestine along the Jordan River which Israel did not control prior to 1967. It represents roughly 18% of the total area of the British Mandate of Palestine, making it the largest Palestinian territorial acquisition in the War. It is home to many Ancient Jewish and Christian sites/cities like Nablus (Shchem), Bethlehem, Hebron, and Jericho.

Gaza Strip: This is a very small strip of territory that Egypt held from 1949-1967. It remained under Israeli military control until 1993 when it was given to the Palestinian Authority as part of the Oslo Accords.

Sinai Peninsula: Easily the largest piece of territory (60,000 km square) that Israel acquired during the Six-Day War, the Sinai Peninsula is larger than the entire British Mandate of Palestine. It was used by Israelis as a resort area and for its oil reserves until the territory was returned to Egypt over the course of three years (1979-1982) for peace and a continuous stream of oil.

Eastern Bank of the Sea of Galilee: This is the smallest peace of land (5 km square) that Israel recaptured and is the only territory from the British Mandate of Palestine that the Palestinians have never explicitly claimed. From 1949-1967, Syria held this piece of land, giving Syria direct access to a small portion of the Sea of Galilee and thus Israel/Palestine's main water source.

Golan Heights: This is a Syrian Mountain Range just north of western Jordan. This territory is small, but strategic, giving Israel a position where Syria cannot take military advantage of it. Currently, UNDOF monitors the border between the Golan Heights and Syria.