Electrocyclic reaction
The above diagram shows two examples. For the 5,6-dimethylcyclohexa-1,3-diene (top row of diagram), only a disrotatory mode would result in p-orbitals having the same symmetry as the HOMO of hexatriene. The two p-orbitals rotate in opposite directions. For the 3,4-dimethylcyclobutene (bottom row of diagram), only a conrotatory mode would result in p-orbitals having the same symmetry as the HOMO of butadiene. The p-oribtals rotate in the same direction.