Exodus 12:16

And on the first day there shall be a holy congregation, and on the seventh day there shall be to you a holy congregation. No work shall be done among you, only that which must be done for every one's eating may be done by you.

NO MANNER OF WORK SHALL BE DONE IN THEM. Rashi commented: “Even by the agency of others.”
I do not understand this. If these “others” are Israelites, they themselves are commanded not to work on the Festival, and I am not bound to ensure that my work is not done through them. It is only where one deceives another in a matter which is prohibited — whether it be in the deceiver’s work or in that of the deceived that the deceiver transgresses the prohibition, Before the blind do not put a stumbling-block. And if these “others” are non-Israelites, we are by law of the Torah not admonished at all against their working either on a Festival or on a Sabbath, except that there is a prohibition by the Rabbis if we tell him [the non-Israelite] to do the work, just as the Rabbis have said: “Telling a non-Israelite [to do work on the Sabbath or Festival] is prohibited by law of the Rabbis,” and this is a principle clearly established in the Gemara. [How then could Rashi derive this principle of prohibiting telling a non-Israelite to do work for us on a Festival from a verse in the Torah, when it is only prohibited by Rabbinic law?]
However, I have found this text in the Mechilta: “No manner of work shall be done in them. This means that neither you nor your fellow-Israelite shall do any work, nor shall a non-Israelite do your work. You so interpret it to mean that neither you nor your fellow-Israelite shall do any work, nor shall a non-Israelite do your work, but perhaps it rather means that neither you nor your fellow-Israelite shall do any work, and the non-Israelite shall not do even his own work! Scripture therefore says, Six days shall work be done.. See my Hebrew commentary, p. 330, for a detailed explanation of how the principle discussed is derived from the language of the verse. This teaches that neither you nor your fellow-Israelite shall do any work [on the Sabbath], but the non-Israelite may do his own work. These are the words of Rabbi Yashiya. Rabbi Yonathan says that there is no need for this proof. Has it not already been said, Six days shalt thou labour, and do all thy work? Now by the syllogism of kal vachomer, we proceed as follows: If on the Sabbath, in regard to which the Torah is so strict, you are not admonished against a non-Israelite’s work as you are against your own work, [it is logical to assume that on a Festival-day, in regard to which the Torah is not so strict — inasmuch as preparation of …

אך אשר יאכל לכל נפש, the permission to cook on the festivals is the reason that the work prohibition in connection with festivals is always worded as כל מלאכת עבודה לא תעשו instead of כל מלאכה לא תעשה as on the Sabbath or Day of Atonement, which means: “no manner of work must be performed, [preparation of food involving use of fire being included. Ed.]

כל מלאכה, “all manner of work;” Rashi explains the word כל, “all,” as including work performed for the Israelite in question on his behalf by others. Rabbi Moshe had difficulty with Rashi’s commentary here seeing that the Talmud in tractate Shabbat folio 150 states that the prohibition to ask gentiles to perform work for us on the Sabbath is of rabbinic origin, so how could it have been described from a verse in the Torah? We must therefore assume that what Rashi meant is that he understood the word כל as only what is known as an assmachta, a “support” from a word in the text, not a direct command. Alternately, what Rashi meant when he wrote: על ידי אחרים, “by others,” referred to other members of his household such as sons or daughters who are still minors. Although this prohibition has been spelled out in Exodus 20,10 in the Ten Commandments, this might have been understood as referring only to work performed on the Sabbath, the penalty for which is far more severe. The word כל, here therefore includes days of a festival.

הוא לבדו יעשה לכם, “only it may be performed for you.” The apparently extraneous word ל-בדו is meant to remind us that the first day of Passover must not occur (i.e. The rabbis arranging the calendar must see to this) on either the second, the fourth, or the sixth day of the week. [The reason is connected to the inconvenience caused the people then with the days on which Rosh Hashanah or Yom Kippur would occur. Ed.]