How long does Hell burn for?

Malachi wrote that the wicked will be “burned up”, they will have “neither root nor branch” and will be “ashes” under the feet of the saved:

Malachi 4:1-3 King James Version (KJV)
1 For, behold, the day cometh, that shall burn as an oven; and all the proud, yea, and all that do wickedly, shall be stubble: and the day that cometh shall burn them up, saith the Lord of hosts, that it shall leave them neither root nor branch.
2 But unto you that fear my name shall the Sun of righteousness arise with healing in his wings; and ye shall go forth, and grow up as calves of the stall.
3 And ye shall tread down the wicked; for they shall be ashes under the soles of your feet in the day that I shall do this, saith the Lord of hosts.

Peter wrote that Sodom and Gomorrha were turned to ashes, and are an example to those who live ungodly:

2 Peter 2:6 King James Version (KJV)
6 And turning the cities of Sodom and Gomorrha into ashes condemned them with an overthrow, making them an ensample unto those that after should live ungodly;

Jude writes that Sodom and Gomorrha suffered as an example for us the “vengeance of eternal fire” but are not still burning eternally today:

Jude 1:7 King James Version (KJV)
7 Even as Sodom and Gomorrha, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire.

Jesus stated that both soul and body can be destroyed in hell:

Matthew 10:28 King James Version (KJV)
28 And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell.

People believe that Jesus described hell as eternal fire “where their worm dieth not” and the “fire is not quenched”:

Mark 9:43-44 King James Version (KJV)
43 And if thy hand offend thee, cut it off: it is better for thee to enter into life maimed, than having two hands to go into hell, into the fire that never shall be quenched:
44 Where their worm dieth not, and the fire is not quenched.

However, Isaiah describes looking upon “the carcases of the men” as “their worm shall not die, neither shall their fire be quenched” so Jesus is not referring to an eternal fire of hell:

Isaiah 66:24 King James Version (KJV)
24 And they shall go forth, and look upon the carcases of the men that have transgressed against me: for their worm shall not die, neither shall their fire be quenched; and they shall be an abhorring unto all flesh.

The Bible describes Jerusalem burning with a fire that “shall not be quenched” but it is not still burning eternally today:

Jeremiah 17:27 King James Version (KJV)
27 But if ye will not hearken unto me to hallow the sabbath day, and not to bear a burden, even entering in at the gates of Jerusalem on the sabbath day; then will I kindle a fire in the gates thereof, and it shall devour the palaces of Jerusalem, and it shall not be quenched.

A Psalmist writes in a little while “the wicked shall not be”:

Psalm 37:10 King James Version (KJV)
10 For yet a little while, and the wicked shall not be: yea, thou shalt diligently consider his place, and it shall not be.

Jesus said there is an “everlasting punishment” and “life eternal”:

Matthew 25:46 King James Version (KJV)
46 And these shall go away into everlasting punishment: but the righteous into life eternal.

This “everlasting” punishment is death, which is the “wages of sin”:

Romans 6:23 King James Version (KJV)
23 For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.

In Revelation, the place of “fire and brimstone” known to us as Hell, is called “the second death”:

Revelation 21:8 King James Version (KJV)
8 But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death.