Leviticus 1:4

And he shall lay his right hand with firmness upon the head of the sacrifice, that it may be acceptable from him to propitiate on his behalf.

He will place his hand [singular] It seems from a literal interpretation of the verse that he places a single hand (for we cannot assume that the scapegoat [16:21] resembles the other offerings, insofar as there Scripture specifically mentions how many hands are to be placed). However, the Exegetes, upon whom we rely, have determined that all laying on of hands involves both hands [Yoma 36a]. The animal which atones for an emergent impulse is called a burnt offering [literally: an arising]. Similarly, the animals brought to atone for sin and guilt are called sin-offerings and guilt-offerings, respectively.

it will be accepted he will obtain God’s good will.

to atone for him to release him from the punishment due him

AND HE SHALL LAY HIS HAND. This means his two hands, for we find it stated: and Aaron and his sons shall lay their hands upon the head of the bullock; and Aaron and his sons shall lay their hands upon the head of the ram,, Verse 15. and the Rabbis interpreted it to mean: “the hands of each and every individual.” Thus [it is clear that] both hands were required for it. In the case of the goat designed to be sent [to Azazel] it is expressly stated, And Aaron shall lay both his hands upon the head of the live goat. If so, I do not know why Scripture wrote “his hand” [in the singular] in all other cases of the laying of hands. Perhaps it is for the purpose of deriving therefrom what the Rabbis have interpreted: “His hand — and not the hand of his proxy.” For had it been written “his hands” [in the plural we would have interpreted it] to require the laying of both hands, and we would not have been able to exclude the proxy. But now that [we derive from other verses that] both hands must be laid upon the offering, [we must conclude that] He only wrote the singular [indicating the hands of only one person], to exclude a proxy, for although a man’s proxy is like the man himself in all other places, we should not consider him so in the case of the laying of hands. In Torath Kohanim we find: 4:4. “And Aaron shall lay both his hands. This teaches that the laying of hands upon the offering must be done with both hands, and forms the general rule for all cases of laying of hands, that they be done with both hands.”

לכפר עליו, “to make atonement for him.” When someone has eaten forbidden fats, inadvertently, he must bring an offering as atonement. If he is in doubt if he has eaten forbidden fat he must bring an offering known as asham taluy, an offering which suspends his status vis a vis G–d until the doubt has been removed. If it turns out that he had not eaten forbidden fat that is the end of the matter. If it turns out that he did eat forbidden fat, he must bring the additional sin offering. Sometimes it happens that a person was convinced that what he ate was permissible, whereas in fact it was not. In such an event, offering a burnt offering will achieve atonement on his behalf. This is the kind of burnt offering described in our verse.