Using psi(3686)->pi(0)h(c) decays from a data sample of (27.12 +/- 0.14)x10(8) psi(3686) events collected by the BESIII detector at the BEPCII collider, h(c) radiative decays to multiple light hadrons below 2.8 GeV/c(2)-gamma pi(+)pi(-), gamma pi(+)pi(-)eta, gamma 2(pi(+)pi(-)), and gamma p (p) over bar -are observed for the first time, each with a significance greater than 5 sigma. The corresponding branching fractions are measured. Furthermore, intermediate states are investigated, leading to the first observation of the decay process of h(c)-> gamma f(2)(1270)->gamma pi(+pi-) with a significance of 5.1 sigma. This observation represents the first instance of h(c) radiative decay to a tensor state.