What is the longest barrel on a M-16 in the military?

All variants of the M16 use a 20" barrel. As has already been pointed out, there is no point to having a barrel longer than this for a 5.56mm bullet.

The M4/M4A1 has a 14.5" barrel.

The Mk18 and CQBR have a 10.5" barrel, and the Mk12 has an 18" barrel. None of these weapons are commonly used outside of specialized units that need these specific modifications for one reason or another.

For the M-16, it is a 20in barrel. There are not any barrels longer than that for the M-16.

There really isn't much "advantage" to using a longer barrel on a modern fire arm, because almost all of the propellant is burnt before it reaches the end of a 20" barrel.

A black powder rifle would shoot farther from a longer barrel because it burns slower.

The 20" barrel is the standard length on the M-16 and the M-4 is 14 1/2"

Not sure what you mean by "taking advantage"

yes there are longer barrels

but the M-16 is was made to work well on open ground, thick jungle and buildings

and longer barrel would be more accurate long distance shooting

but would be hard to move around in buildings and forest