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אם על תורה יקריבנו IF HE OFFER IT FOR A THANKSGIVING — i.e., if he brings it on account of (על) a matter that requires thanksgiving (תודה): on account of a miraculous deliverance that was wrought for him, as being, for instance, one of those who have made a sea-voyage. or travelled in the wilderness, or had been kept in prison, or if he had been sick and was now healed, all of whom are bound to offer thanks-giving, since it is written with reference to them, (Psalms 107:8, 15, 21, 31) “Let them offer thanksgiving to the Lord for His goodness, and for His wonderful works to the children of men!” (cf. Rashi on those vv. and on vv. 4, 10, 17 and 23 of that chapter; see also Berakhot 54b) — if it is on account of one of these things that he vowed those peace offerings, they are “peace offerings for acknowledgement” and require the offering of bread that is mentioned in the section, and may not be eaten beyond a period of one day and one night as it is here set forth (v. 15) [whilst other שלמים may be eaten at any time during two days and the intervening night].

THEN HE SHALL OFFER ‘AL’ THE OFFERING OF THANKSGIVING. The commentators⁹⁰So explained by Ibn Ezra. have explained the word al as meaning “with” — with the offering of thanksgiving. Similarly, ‘al’ the cakes of leavened bread⁹¹Verse 13. means “with them.” The correct interpretation appears to me that the word al is here to be understood in its ordinary sense [i.e., “upon”], meaning that he should add bread “upon” the offering. Similarly, ‘al’ the cakes of leavened bread he shall present his offering,⁹¹Verse 13. means that he is to bring cakes of leavened bread, and adding “upon” them he is to bring his offering, which is the unleavened bread mentioned [in Verse 12 before us] — all these breads [thirty unleavened cakes and ten leavened ones] he is to bring upon the offering [of thanksgiving]. Scripture thus made the leavened bread the chief part of the offering, “adding” upon it the rest of the bread [i.e., the unleavened bread, by stating “upon the cakes of leavened bread he shall present his offering,” which means “his unleavened bread”], because the unleavened breads are more than all the other kinds.⁹²Flour comprising twenty tenths of an ephah (see Note 95) was divided equally for the baking of the unleavened and leavened breads. The unleavened breads were of three kinds [cakes, wafers, and cakes of flour saturated with oil — as mentioned in Verse 12] each consisting of ten, thus making thirty unleavened breads. The leavened breads were ten. Thus while fewer in number, the leavened breads were yet larger, since the same amount of flour was used for the total amount of unleavened breads — thirty — as for the ten leavened breads. Of these four kinds of breads, one of each was given to the priest and the rest were eaten by the owner of the offering and his family. Scripture changed the expression, stating, [he shall present his offering] of his peace-offerings for thanksgiving⁹¹Verse 13. [while here in Verse 12 it merely says, the offering of thanksgiving], in order to allude to the Rabbis’ interpretation regarding it, namely that the bread does not become holy in itself [in the sense that it cannot be redeemed, or that it becomes invalid if carried outside the wall of the city, etc.] until the offering is slaughtered, and [also] that it should be slaughtered “upon” it [the bread], that is to say, with the intention that the bread should become holy with it [the offering].
Now Rashi wrote: “Then he shall bring with the offering of thanksgiving four sorts of bread: cakes, wafers, and cakes mingled with oil — these three kinds being of unleavened bread. And it further states, with cakes of leavened bread,⁹¹Verse 13. [thus making four kinds], and each kind consisted of ten cakes. Thus it is explained in Tractate Menachoth.⁹³Menachoth 77 a. And their total measure was five Jerusalem seahs, which are six measures according to the Wilderness measure,⁹⁴The Jerusalem measure was one sixth larger than that of the wilderness. Hence six seahs of Wilderness measure made five seahs of Jerusalem measure. or twenty tenths [of the ephah].”⁹⁵An ephah is three seahs. Six seahs thus make two ephahs. Since in each ephah there are ten tenths [of the ephah], the two ephahs [comprising the six seahs] make twenty tenths of the ephah. Now the Rabbi [Rashi] did not mention in connection with these twenty tenths [of flour] that ten of them were for the leavened cakes, a tenth for each one, and the other ten tenths for the unleavened ones, thus making three unleavened cakes to each tenth of flour.⁹⁶There were three kinds of unleavened cake, each consisting of ten cakes, thus totaling thirty. Thus since thirty cakes were made out of the total of ten tenths of an ephah, it follows that three cakes were made out of each tenth. The Rabbis interpreted that this is so on the basis of the verse, ‘al’ cakes of leavened bread,⁹¹Verse 13. [which they explained⁹³Menachoth 77 a. as meaning]: “‘Corresponding to’ [the amount of flour used in the preparation of the ten] leavened cakes, use the same amount to bring therefrom [the thirty] unleavened cakes. Thus there were twenty tenths [of an ephah of flour], ten for the leavened cakes and ten for the unleavened. Ten tenths were used for the leavened ones, thus making one tenth of flour for each of [the ten] leavened cakes, and ten tenths for the unleavened ones, thus making three cakes to one tenth of flour. Thus there were forty cakes altogether.”

אם על תודה, if a person had made a vow using the expression תודה instead of using the expression שלמים to describe what he vowed to bring. The most common occasion when people make such a vow is when they have been saved from imminent danger. The sages in Berachot 54 described the four types of dangers which qualify for the party who has been saved to offer such a “thanksgiving” offering, תודה. The total number of challot which this offering consists of are 40. Here we are told all the details.