The emission of neutron pairs from the neutron-rich N = 12 isotones C-18 and O-20 has been studied by high-energy nucleon knockout from N-19 and O-21 secondary beams, populating unbound states of the two isotones up to 15 MeV above their two-neutron emission thresholds. The analysis of triple fragment-n-n correlations shows that the decay N-19(-1p)18C*-> C-16 + n + n is clearly dominated by direct pair emission. The two- neutron correlation strength, the largest ever observed, suggests the predominance of a C-14 core surrounded by four valence neutrons arranged in strongly correlated pairs. On the other hand, a significant competition of a sequential branch is found in the decay O-21(-1n)O-20*-> O-18 + n + n, attributed to its formation through the knockout of a deeply bound neutron that breaks the O-16 core and reduces the number of pairs.
