Suppose that trans-cis-trans-2,4,6-octatriene is converted to  under thermal conditions.  Since the substrate octatriene is a "4n + 2" molecule, the Woodward–Hoffmann rules predict that the reaction happens in a disrotatory mechanism.
Since thermal electrocyclic reactions occur in the HOMO, it is first necessary to draw the appropriate molecular orbitals. Next, the new carbon-carbon bond is formed by taking two of the p-orbitals and rotating them 90 degrees (see diagram). Since the new bond requires constructive overlap, the orbitals must be rotated in a certain way. Performing a disrotation will cause the two black lobes to overlap, forming a new bond. Therefore, the reaction with octatriene happens through a disrotatory mechanism.
In contrast, if a conrotation had been performed then one white lobe would overlap with one black lobe.  This would have caused destructive interference and no new carbon-carbon bond would have been formed.
In addition, the cis/trans geometry of the product can also be determined. When the p-orbitals were rotated inwards it also caused the two methyl groups to rotate upwards. Since both methyls are pointing "up", then the product is .