The NVT Monte Carlo simulation results are reported for a model of two-dimensional (2D) chemically associating fluid with six attractive sites per monomer disc. Three of these sites are of the type alpha and the other three of the type beta. The sites alpha and beta are fixed inside a hard core, they follow each other anticlockwise, with a ＇valence＇ angle of 60 degrees. It is assumed that only alpha+beta site-site association of two different discs occurs. Complex formation, dependent on the density and association energy, is much more sophisticated, in comparison to previously studied models of dimerizing and polymerizing discs. An analysis of complexes in terms of the fractions of singly, doubly,..., hers-bonded particles is performed, and the dimensions and distributions of complexes are studied. We obtained the pair distribution functions of particles and structure factor in the fluid layer. The model was inspired by experiments on visualization of organic monolayers in the framework of scanning tunneling microscopy (STM). Currently it yields a preliminary insight into the molecular organization of crystal violet molecules on the iodine covered (111) single-crystal surface plane observed experimentally. Extensions of the model and methodology are discussed.