Search for new hadronic decays of h(c) and observation of h(c) -> p(p)over-bar eta

A search for the hadronic decays of the h(c) meson to the final states p (p) over bar pi(+)pi(-)pi(0), p (p) over bar eta and p (p) over bar pi(0) via the process psi(3686) -> pi(0)(h)c is performed using (4.48 +/- 0.03) x 10(8) psi(3686) events collected with the BESIII detector. The decay channel h(c) -> p (p) over bar eta is observed for the first time with a significance greater than 5 sigma and a branching fraction of (6.41 +/- 1.74 +/- 0.53 +/- 1.00) x 10(-4), where the uncertainties are statistical, systematic, and that from the branching fraction of psi(3686) -> pi(0)(h)c. Strong evidence for the decay h(c) p (p) over bar pi(+)pi(-)pi(0) is found with a significance of 4.9 sigma and a branching fraction of (3.84 +/- 0.83 +/- 0.69 +/- 0.58) x 10(-3). The significances include systematic uncertainties. No clear signal of the decay h(c) -> p (p) over bar pi(0) is found, and an upper limit of 6.59 x 10(-4) on its branching fraction is set at the 90% confidence level.