In this article the operation of a two-phase cryogenic avalanche detector (CRAD) in Ar with optical readout using combined multiplier based on thick gas electronic multipliers (THGEMs) and a matrix of Geiger-mode avalanche photodiodes (GAPD) has been studied. The successful operation of such a detector when irradiated by x-ray photons with the average energy of 20 keV was demonstrated. The yield of such combined multiplier amounted at about 100 photoelectrons at THGEM avalanche gain of 160. In addition, the spatial resolution of the detector was measured; it turned out to be 1 mm