The collective motion of dust particles during the mode-coupling–induced melting of a two-dimensional plasma crystal is explored in molecular-dynamics simulations. The crystal is compressed horizontally by an anisotropic confinement. This compression leads to an asymmetric triggering of the mode-coupling instability which is accompanied by alternating chains of in-phase and anti-phase oscillating particles. A new order parameter is proposed to quantify the synchronization with respect to different directions of the crystal. Depending on the orientation of the confinement anisotropy, mode-coupling instability and synchronized motion are observed in one or two directions. Notably, the synchronization is found to be direction dependent. The good agreement with experiments suggests that the confinement anisotropy can be used to explain the observed synchronization process.