We report measurements of charmonia produced in two-photon collisions and decaying to four-meson final states, where the meson is either a charged pion or a charged kaon. The analysis is based on a 395fb^{-1} data sample accumulated with the Belle detector at the KEKB electron-positron collider. We observe signals for the three C-even charmonia eta_c(1S), chi_{c0}(1P) and chi_{c2}(1P) in the pi^+pi^-pi^+pi^-, K^+K^-pi^+pi^- and K^+K^-K^+K^- decay modes. No clear signals for eta_c(2S) production are found in these decay modes. We have also studied resonant structures in charmonium decays to two-body intermediate meson resonances. We report the products of the two-photon decay width and the branching fractions, Gamma_{gamma gamma}B, for each of the charmonium decay modes.
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