A cryogenic target system for preparing the dense gaseous samples is established on a two-stage light-gas gun and is applied to study the equation of state of hydrogen-helium mixture at higher pressures and at high temperatures by means of the multi-shock technique. The recorded optical radiation signal clearly indicates the beginning moments of the third-, fourth-, sixth-, eighth-, and tenth-shock processes, which are in good agreement with the predictions of the Mansoori-Canfield-Ross variational perturbation theory up to the observed ultimate state of 104 GPa.