What is the significance of the 'Voice' that they heard in the Garden? What was Hashem doing there?
Rashi, Seforno and Targum Yonasan 1 : Hashem, Kevayachol, was walking round the Garden, as He did every day, seeing to its needs, and that is what Adam and Chavah heard and went to hide.
Ramban: Whenever the term "Mis'halech" 2 (the reflexive) is used in connection with Hashem, it refers to a revelation (or the departure) of the Shechinah, accompanied by a powerful wind. Here too, the Shechinah was accompanied by a strong 3 wind. Refer to 3:8:2:2 and 3:8:2:1 .
This seems to tally with a list of commentaries cited by the Ramban who learn like this - in fact, it was the voice that they heard walking around the garden.
Rosh: The angels claimed that Adam was like a Meis ("Mis'halech" is a contraction of Meis Holech) - to which Hashem replied, "le'Ru'ach ha'Yom" - Arvi'ach (I will widen) his day to be like Mine (to live a thousand years).
The wind here was not a powerful one, so as not to frighten and confuse Adam and Chavah.
What is the meaning of the words, "le'Ru'ach ha'Yom"?
Rashi: It refers to the west direction, where the sun was about to set at the end of the day. 1
Ramban: It refers to the strong wind that accompanied the Shechinah. Refer to 3:8:2:2 .
Gur Aryeh: The sun is called day, since it is the cause of daytime. Adam sinned in the tenth hour [of the day, counting from sunrise]; so the sun was in the west (Rashi, based on Sanhedrin 38b).
Why did Adam and Chavah hide when they heard the Voice of Hashem in the Garden?
Seforno: In fulfillment of the Pasuk, "And He (Hashem) shall not see in you any nakedness" (Devarim 23:15).
Targum Yonasan: They were actually trying to hide from Hashem out of shame (as is evident from his explanation in 3:10). 1
Since they now had a Yetzer ha'Ra, whose strategy is to make a person believe that he can hide from Hashem.
How is it possible to hide from Hashem?
Maharal (Chidushei Agados, Vol. 3. p. 153, to Sanhedrin 38b): The deeper meaning is that Adam wanted to remove himself from Hashem's [Providence]; Adam felt that man should fall into the natural order. This is what Chazal mean that Adam extended his Orlah (ibid.); 1 the Orlah represents the covering caused by nature, and Milah is above nature. 2
Refer to 3:8:3:2* .
The Gemara (Chulin 139b) asks, "What is the source in Torah for Haman?", and it answers with our verse, "ha'Min ha'Etz." What is the connection?
Da'as Zekenim: Hashem said that it would have been proper to hang Adam on the tree; but rather, Hashem would suspend and preserve [that judgment], and later hang Haman on it.
QUESTIONS ON RASHI
Rashi writes: "'They heard' - the voice of Hashem... that He was walking (Mis'halech) in the garden." It seems that Rashi is merely adding the phrase "that He was." What is Rashi explaining?
Gur Aryeh: We might have understood that they heard the voice [of Hashem] moving in the garden; but then the appropriate verb would be "Holech." The reflexive verb "Mis'halech" shows that they heard Hashem Himself walking in the garden. 1
The verb form "Hispa'el" indicates that the verb's subject does something by itself, willingly and autonomously. A voice does not move of its own accord, but is rather set in motion by another.