Active region NOAA 11283 produced two X-class flares on 6 and 7 September 2011 that have been well studied by many authors. The X2.1 class flare occurred on September 6, 2011 and was associated with the first of two homologous white light flares produced by this region, but no sunquake was found with it despite the one being detected in the second flare of 7 September 2011. In this paper we present the first observation of a sunquake for the 6 September 2011 flare detected via statistical significance analysis of egression power and verified via directional holography and time-distance diagram. The surface wavefront exhibits directional preference in the north-west direction We interpret this sunquake and the associated flare emission with a combination of a radiative hydrodynamic model of a flaring atmosphere heated by electron beam and a hydrodynamic model of acoustic wave generation in the solar interior generated by a supersonic shock. The hydrodynamic model of the flaring atmosphere produces a hydrodynamic shock travelling with supersonic velocities towards the photosphere and beneath. For the first time we derive velocities (up to 140 km/s) and onset time (about 50 seconds after flare onset) of the shock deposition at given depths of the interior. The shock parameters are confirmed by the radiative signatures in hard X-rays and white light emission observed from this flare. The shock propagation in the interior beneath the flare is found to generate acoustic waves elongated in the direction of shock propagation, that results in an anisotropic wavefront seen on the solar surface. Matching the detected seismic signatures on the solar surface with the acoustic wave front model derived for the simulated shock velocities, we infer that the shock has to be deposited under an angle of about 30 to the local solar vertical. Hence, the improved seismic detection technique combined with the double hydrodynamic model reported in this study opens new perspectives for observation and interpretation of seismic signatures in solar flares.