The rule can be used to understand the stability of completely conjugated monocyclic hydrocarbons (known as annulenes) as well as their cations and anions.
The best-known example is benzene (CH) with a conjugated system of six π electrons, which equals 4n + 2 for n = 1. The molecule undergoes substitution reactions which preserve the six π electron system rather than addition reactions which would destroy it. The stability of this π electron system is referred to as aromaticity. Still, in most cases, catalysts are necessary for substitution reactions to occur.
The cyclopentadienyl anion () with six π electrons is planar and readily generated from the unusually acidic cyclopentadiene (pK 16), while the corresponding cation with four π electrons is destabilized, being harder to generate than a typical acyclic pentadienyl cations and is thought to be antiaromatic. Similarly, the tropylium cation (), also with six π electrons, is so stable compared to a typical carbocation that its salts can be crystallized from ethanol. On the other hand, in contrast to cyclopentadiene, cycloheptatriene is not particularly acidic (pK 37) and the anion is considered nonaromatic.  The cyclopropenyl cation ()  and the triboracyclopropenyl dianion () are considered examples of a two π electron system, which are stabilized relative to the open system, despite the angle strain imposed by the 60° bond angles.
Planar ring molecules with 4n π electrons do not obey Hückels rule, and theory predicts that they are less stable and have triplet ground states with two unpaired electrons. In practice such molecules distort from planar regular polygons. Cyclobutadiene (CH) with four π electrons is stable only at temperatures below 35 K and is rectangular rather than square. Cyclooctatetraene (CH) with eight π electrons has a nonplanar "tub" structure. However the dianion  (cyclooctatetraenide anion), with ten π electrons obeys the 4n + 2 rule for n = 2 and is planar, while the 1,4-dimethyl derivative of the dication, with six π electrons, is also believed to be planar and aromatic. The Cyclononatetraenide anion () is the largest all-cis monocyclic annulene/annulenyl system that is planar and aromatic.  These bond angles (140°) differ significantly from the ideal angles of 120°.  Larger rings possess trans bonds to avoid the increased angle strain.  However, 10 to 14-membered systems all experience considerable transannular strain.  Thus, these systems are either nonaromatic or experience modest aromaticity.  This changes when we get to [[Cyclooctadecanonaene|[18]annulene]], with (4×4) + 2 = 18 π electrons, which is large enough to accommodate six interior hydrogen atoms in a planar configuration (3 cis double bonds and 6 trans' double bonds).  Thermodynamic stabilization, NMR chemical shifts, and nearly equal bond lengths all point to considerable aromaticity for [18]annulene.
The (4n+2) rule is a consequence of the degeneracy of the π orbitals in cyclic conjugated hydrocarbon molecules. As predicted by Hückel molecular orbital theory, the lowest π orbital in such molecules is non-degenerate and the higher orbitals form degenerate pairs. For benzene the lowest π orbital is non-degenerate and can hold 2 electrons, and the next 2 π orbitals form a degenerate pair which can hold 4 electrons. The 6 π electrons in benzene therefore form a stable closed shell in a regular hexagonal molecule.
However for cyclobutadiene or cyclooctatrene with regular geometries, the highest molecular orbital pair is occupied by only 2 π electrons forming a less stable open shell. The molecules therefore stabilize by geometrical distortions which separate the degenerate orbital energies so that the last two electrons occupy the same orbital, but the molecule as a whole is less stable in the presence of such a distortion.