1 This chapter is essentially about mediation. The people are getting ready to meet with God, receive the Law from him, and enter into a covenant with him. All of this required mediation and preparation. Through it all, Israel will become God’s unique possession, a kingdom of priests on earth—if they comply with his Law. The chapter can be divided as follows: vv. 1–8 tell how God, Israel’s great deliverer promised to make them a kingdom of priests; this is followed by God’s declaration that Moses would be the mediator (v. 9); vv. 10–22 record instructions for Israel to prepare themselves to worship Yahweh and an account of the manifestation of Yahweh with all the phenomena; and the chapter closes with the mediation of Moses on behalf of the people (vv. 23–25). Having been redeemed from Egypt, the people will now be granted a covenant with God. See also R. E. Bee, “A Statistical Study of the Sinai Pericope,” Journal of the Royal Statistical Society 135 (1972): 406–21.
2 The construction uses the infinitive construct followed by the subjective genitive to form a temporal clause.
3 Heb “on this day.”

In other versions

On the third new moon after the people of Israel had gone out of the land of Egypt, on that day they came into the wilderness of Sinai.

On the first day of the third month after the Israelites left Egypt—on that very day—they came to the Desert of Sinai.

In the third month from the very day the Israelites left the land of Egypt, they came to the Sinai Wilderness.

Exactly two months after the Israelites left Egypt, they arrived in the wilderness of Sinai.

In the third month after the Israelites went out from the land of Egypt, on this day they came to the Sinai desert.

In the third month, when the children of Israel were gone forth out of the land of Egypt, the same day came they into the wilderness of Sinai.

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