Wavevector-selective impulsive excitation of phonon-polaritons by a spectrally broad femtosecond transient grating produces wavepackets propagating in opposite directions. The photons in spectrally narrow probe pulses are scattered from these elementary excitations in lithium niobate (LiNbO3). Both elastically and inelastically scattered photons are simultaneously detected in a spectrometer. The Stokes- and anti-Stokes shifted probe pulses uniquely determine the propagation direction of the detected polariton wavepacket components and correspond to creation or annihilation of phonon-polaritons. Our experiments with spectrally broad pump and spectrally narrow probe pulses allows dissecting the four-wave-mixing process into two sequential stimulated Raman scattering events.