Driving four-wave mixing (FWM) processes with extreme ultraviolet (EUV) pulses could enable experimental approaches that have the potential to provide unique information on dynamics and correlations. In this work, we demonstrate inelastic FWM obtained by noncollinear mixing of two EUV pulses with different photon energies and an optical pulse in a diamond sample. This three-pulse interaction leads to the emission of an optical signal, propagating in the phase-matching direction and blue shifted by the photon energy difference of the two EUV pulses. The presented results demonstrate the feasibility of experiments such as the soft X-ray analogue of coherent anti-Stokes Raman scattering, so far only theoretically conceived [Phys. Rev. Lett. 89, 043001 (2002)], which can be further extended for studying vibrational and electronics dephasing in solid, liquid, or gaseous samples.