Question: 
I have a technical question on 2 Samuel 15:7.  
Did forty years or four years passed after Absalom
opted to pay his vow in Hebron, first asking leave
from David his father? 

Answer: At first the question caught me in a quandary.
I did not have a problem with the translation, it
appeared correct.
So, I had to figure my times and see what I was
missing.
The Scripture records Absalom in Geshur in 2Samuel
13:37-39:
13:37 But Absalom fled, and went to Talmai, the son of
Ammihud, king of Geshur. And David mourned for his son
every day.
13:38 So Absalom fled, and went to Geshur, and was
there three years.
13:39 And the soul of king David longed to go forth
unto Absalom: for he was comforted concerning Amnon,
seeing he was dead.
Your question concerns the passage in 2Samuel 15 given
below in its entirety. Evidently Absalom was in Geshur
at best guess between 1030 and 1027 A.D.. The acts of
chapter 15 probably span a period between 1024 and
1021 A.D. a period of about three years. He did not
have the patience to spend forty years undermining the
king as described in chapter 15. The time span between
Absalom’s supposed vow would be less than nine years,
but likely more than four. So what is the answer? I
think the most likely answer to the forty year
reference was that he acted in the fortieth year of
his life. This makes the most sense to me.
15:1 And it came to pass after this, that Absalom
prepared him chariots and horses, and fifty men to run
before him.
15:2 And Absalom rose up early, and stood beside the
way of the gate: and it was so, that when any man that
had a controversy came to the king for judgment, then
Absalom called unto him, and said, Of what city art
thou? And he said, Thy servant is of one of the tribes
of Israel.
15:3 And Absalom said unto him, See, thy matters are
good and right; but there is no man deputed of the
king to hear thee.
15:4 Absalom said moreover, Oh that I were made judge
in the land, that every man which hath any suit or
cause might come unto me, and I would do him justice!
15:5 And it was so, that when any man came nigh to him
to do him obeisance, he put forth his hand, and took
him, and kissed him.
15:6 And on this manner did Absalom to all Israel that
came to the king for judgment: so Absalom stole the
hearts of the men of Israel.
15:7 And it came to pass after forty years, that
Absalom said unto the king, I pray thee, let me go and
pay my vow, which I have vowed unto the LORD, in
Hebron.
15:8 For thy servant vowed a vow while I abode at
Geshur in Syria, saying, If the LORD shall bring me
again indeed to Jerusalem, then I will serve the LORD.
15:9 And the king said unto him, Go in peace. So he
arose, and went to Hebron.
15:10 But Absalom sent spies throughout all the tribes
of Israel, saying, As soon as ye hear the sound of the
trumpet, then ye shall say, Absalom reigneth in
Hebron.
15:11 And with Absalom went two hundred men out of
Jerusalem, that were called; and they went in their
simplicity, and they knew not any thing.
15:12 And Absalom sent for Ahithophel the Gilonite,
David's counselor, from his city, even from Giloh,
while he offered sacrifices. And the conspiracy was
strong; for the people increased continually with
Absalom.
15:13 And there came a messenger to David, saying, The
hearts of the men of Israel are after Absalom.
15:14 And David said unto all his servants that were
with him at Jerusalem, Arise, and let us flee; for we
shall not else escape from Absalom: make speed to
depart, lest he overtake us suddenly, and bring evil
upon us, and smite the city with the edge of the
sword.
15:15 And the king's servants said unto the king,
Behold, thy servants are ready to do whatsoever my
lord the king shall appoint.
15:16 And the king went forth, and all his household
after him. And the king left ten women, which were
concubines, to keep the house.
15:17 And the king went forth, and all the people
after him, and tarried in a place that was far off.
15:18 And all his servants passed on beside him; and
all the Cherethites, and all the Pelethites, and all
the Gittites, six hundred men which came after him
from Gath, passed on before the king.
15:19 Then said the king to Ittai the Gittite,
Wherefore goest thou also with us? return to thy
place, and abide with the king: for thou art a
stranger, and also an exile.
15:20 Whereas thou camest but yesterday, should I this
day make thee go up and down with us? seeing I go
whither I may, return thou, and take back thy
brethren: mercy and truth be with thee.
15:21 And Ittai answered the king, and said, As the
LORD liveth, and as my lord the king liveth, surely in
what place my lord the king shall be, whether in death
or life, even there also will thy servant be.
15:22 And David said to Ittai, Go and pass over. And
Ittai the Gittite passed over, and all his men, and
all the little ones that were with him.
15:23 And all the country wept with a loud voice, and
all the people passed over: the king also himself
passed over the brook Kidron, and all the people
passed over, toward the way of the wilderness.
15:24 And lo Zadok also, and all the Levites were with
him, bearing the ark of the covenant of God: and they
set down the ark of God; and Abiathar went up, until
all the people had done passing out of the city.
15:25 And the king said unto Zadok, Carry back the ark
of God into the city: if I shall find favor in the
eyes of the LORD, he will bring me again, and show me
both it, and his habitation:
15:26 But if he thus say, I have no delight in thee;
behold, here am I, let him do to me as seemeth good
unto him.
15:27 The king said also unto Zadok the priest, Art
not thou a seer? return into the city in peace, and
your two sons with you, Ahimaaz thy son, and Jonathan
the son of Abiathar.
15:28 See, I will tarry in the plain of the
wilderness, until there come word from you to certify
me.
15:29 Zadok therefore and Abiathar carried the ark of
God again to Jerusalem: and they tarried there.
15:30 And David went up by the ascent of mount Olivet,
and wept as he went up, and had his head covered, and
he went barefoot: and all the people that was with him
covered every man his head, and they went up, weeping
as they went up.
15:31 And one told David, saying, Ahithophel is among
the conspirators with Absalom. And David said, O LORD,
I pray thee, turn the counsel of Ahithophel into
foolishness.
15:32 And it came to pass, that when David was come to
the top of the mount, where he worshipped God, behold,
Hushai the Archite came to meet him with his coat
rent, and earth upon his head:
15:33 Unto whom David said, If thou passest on with
me, then thou shalt be a burden unto me:
15:34 But if thou return to the city, and say unto
Absalom, I will be thy servant, O king; as I have been
thy father's servant hitherto, so will I now also be
thy servant: then mayest thou for me defeat the
counsel of Ahithophel.
15:35 And hast thou not there with thee Zadok and
Abiathar the priests? therefore it shall be, that what
thing soever thou shalt hear out of the king's house,
thou shalt tell it to Zadok and Abiathar the priests.
15:36 Behold, they have there with them their two
sons, Ahimaaz Zadok's son, and Jonathan Abiathar's
son; and by them ye shall send unto me every thing
that ye can hear.
15:37 So Hushai David's friend came into the city, and
Absalom came into Jerusalem.