Associated production of the Higgs boson with a single top quark proceeds through Feynman diagrams, which are either proportional to the hWW, top-Yukawa, or the bottom-Yukawa couplings. It was shown in literature that the interference between the top-Yukawa and the gauge-Higgs diagrams can be significant, and thus the measurement of the cross sections can help pin down the sign and the size of the top-Yukawa coupling. Here we perform a detailed study with full detector simulations of such a possibility at the LHC-14 within the current allowed range of hWW and top-Yukawa couplings, using h-> b b-bar, ����, ��+ ��-, ZZ* -> 4 l modes. We found that the LHC-14 has the potential to distinguish the size and the sign of the top-Yukawa coupling. Among the channels the h-> b b-bar mode mode provides the best chance to probe the signal, followed by the h -> ���� mode, which has the advantage of a narrow reconstructed mass peak. We also pointed out that the spatial separation among the final-state particles has the potential in differentiating among various values of the top-Yukawa coupling.

28 pages, 13 figures; a comment about NLO correction is added, references added; match the published version