These correlation diagrams indicate that only a conrotatory ring opening of 3,4-dimethylcyclobutene is "symmetry allowed" whereas only a disrotatory ring opening of 5,6-dimethylcyclohexa-1,3-diene is "symmetry allowed". This is because only in these cases would maximum orbital overlap occur in the transition state. Also, the formed product would be in a ground state rather than an excited state.