This paper studies the quantum stereodynamics of the F + HD(v = 0,j= 0) → HD + F/HF + D reaction at the collision energies of 0.52 and 0.87 kcal/mol. The quantum scattering calculations, based on Stark-Werner potential energy surfaces, show that the differential cross sections for the HF(υ' = 2) + D and DF(υ' = 3) + H channels are consistent with the recent theoretical results. Furthermore, the product rotational angular momentum orientation and alignment have been determined for some selected rovibrational states of the HF + D and DF + H channels.