The vibrational nuclear structure in Os isotopes has been the subject of debate for decades. In particular, the nature of the 4+3 level was contested to be double quadrupole phonon ([gamma][gamma]) or a single hexadecapole phonon. The [gamma][gamma] view is based on collective B(E2) values from Coulomb excitation and lifetime studies. The single hexadecapole phonon interpretation is supported by a population of the state in single-proton (t,[alpha]) transfer reaction work and an enhanced E4 matrix element from inelastic scattering of [alpha] particles and protons. The proponents of each point of view offer criticisms to the other, but no new experimental work had been performed recently to aid in a resolution. We set out to add more data to this debate by performing a single-proton (3He,d) transfer reaction experiment. The experiment was performed at the Maier-Leibnitz Laboratory in Garching, Germany. The 30 MeV 3He beams provided by the tandem Van de Graaff accelerator bombarded 185,187Re targets while the Q3D spectrograph analyzed the momenta of light ions and focused them onto a focal plane detector for identification and energy measurements. The spectrograph was rotated to angles between 5° and 50° for the transfer reaction work and cross sections were deduced for excited states in 186,188 Os. Results show a significant 52 +402 p+32 +402 p squared amplitude for the 4+3 level consistent with Quasiparticle Phonon Model calculations predicting a dominant hexadecapole component and a large [gamma][gamma] component.