Luke 4:6-7 How do we read that Satan receives authority over the kingdoms of the world?
Luke 4:6-7 (NIV)
6 And he said to him, “I will give you all their authority and
splendor; it has been given to me, and I can give it to anyone I want
to. 7 If you worship me, it will all be yours.” How are we to read,
"it has been given to me"?
All authority "it has been given to me" shows that Satan exercises his power only by permission.
The question that arises is, "Why God grants this permission?" Remember, in the garden of Eden Satan became jealous of the destined blessing given to Adam and Eve if they obeyed God, and believing that disobedience would bring trouble on them, he maliciously persuaded the woman to taste of the tree of wisdom. So he challenged God publicly in front of all his angelic creatures that Adam and Eve would be better off on their own and that God lied, if they ate the forbidden fruit they would die.
Satan said to Eve.“You surely will not die!
Genesis 3:1-6 (NASB)
1 Now the serpent was more crafty than any beast of the field which
the Lord God had made. And he said to the woman, “Indeed, has God
said, ‘You shall not eat from [a]any tree of the garden’?” 2 The woman
said to the serpent, “From the fruit of the trees of the garden we may
eat; 3 but from the fruit of the tree which is in the middle of the
garden, God has said, ‘You shall not eat from it or touch it, or you
will die.’”
4 The serpent said to the woman, “You surely will not die! 5 For God
knows that in the day you eat from it your eyes will be opened, and
you will be like God, knowing good and evil.” 6 When the woman saw
that the tree was good for food, and that it was a delight to the
eyes, and that the tree was desirable to make one wise, she took from
its fruit and ate, and she gave also to her husband with her, and he
ate.
God could have executed Satan and his two followers, but this was a personal challenge to God, so in his wisdom, God allowed Satan and his two followers to live on for a while and at the same time permitted Adam and Eve to have children before they died. The time provided by God has proven that Satan's accusations are false, mankind under Satan-rule or man-rule has not found any peace or happiness.
Conclusion
This is so because mankind as a whole does not accept God's word, and either knowingly or unknowingly they serve Satan as their god. John stated, "We know that we are of God and that the whole world lies in the power of the evil one."1 John 5:19 (NASB)
Under God's Kingdom, God will exercise his will on earth and do away with Satan, he will be abyssed. (Revelation 20:1-6 Vs3 abyssed NASB) and the evil men will be no more.
Psalm 37:10 NET
10 Evil men will soon disappear; you will stare at the spot where they
once were, but they will be gone.
Psalm 14:1 (NET Bible)
Fools say to themselves, “There is no God.” They sin and commit evil
deeds; none of them does what is right.
Isaiah 11:1-5 (NET Bible)
An Ideal King Establishes a Kingdom of Peace
11 A shoot will grow out of Jesse’s[a] rootstock, a bud will sprout[b]
from his roots. 2 The Lord’s Spirit will rest on him— a Spirit that
gives extraordinary wisdom,[d] a Spirit that provides the ability to
execute plans, a Spirit that produces absolute loyalty to the Lord. 3
He will take delight in obeying the Lord. He will not judge by mere
appearances or make decisions on the basis of hearsay. 4 He will treat
the poor fairly, and make the right decisions for the downtrodden of
the earth. He will strike the earth with the rod of his mouth and
order the wicked to be executed. 5 Justice will be like a belt around
his waist, integrity will be like a belt around his hips.