Why does the Torah need to tell us to work six days? And how can one finish all one's work in one week?
Rashi: What the Torah means is that, when Shabbos arrives, we should consider it as if all our work has been completed. 1
Divrei Eliyahu and Kol Eliyahu: The Gemara in Shabbos 69b rules that, someone who is in the desert and does not know which day is Shabbos is permitted to do as much work as he needs to stay alive - Shabbos included. Consequently, the Torah warns us to remember which day is Shabbos, in order to be able to all our work in six days - also what is needed for Shabbos, and to desist from working on Shabbos. 2
What is the difference between 'Avodah' and 'Melachah'?
Ramban: 'Avodah' refers to work that is not for one's immediate benefit, such as work in the fields; 1 whereas 'Melachah' refers to work from which one benefits immediately, such as preparation of food -- both of which the Torah is now coming to forbid on Shabbos. 2
Ramban: See for example, Shemos 1:14, and Bereishis 4:12 .
Though it permits the latter on Yom-Tov.
Having written "Sheishes Yamim Ta'avod," why does the Torah add "v'Asisa Kol Melachtecha?