Albert Barnes Commentary Psalms 78:54

"And he brought them to the border of his sanctuary, To this mountain, which his right hand had gotten." — Psalms 78:54 (ASV)

And he brought them to the border of his sanctuary - The Septuagint and the Latin Vulgate render this, “to the mountain of his holiness”; that is, his holy mountain. But the reference is rather to the whole land of Canaan. He brought them to the borders of that land—the land of promise—the holy land. They who came out from Egypt did not indeed enter that land, except Caleb and Joshua, but they were conveyed to its borders before all of them fell. It was true also that the people—the Hebrew people—came to the promised land and secured its possession.

Even to this mountain - Mount Zion, for the object of the psalm was to show that the worship of God was properly celebrated there. . The meaning is not that the people who came out of Egypt actually inherited that mountain, but that their descendants—the people of God—had been put in possession of it.

Which his right hand had purchased - Had procured, or obtained possession of. That is, he had secured it by his power.