Every time there is an alpha decay, there is a decrease of the mass number by 4 and atomic number by 2.  Every time there is a beta decay, there is no change in mass number but increase in atomic number by 1.  Therefore, you can determine the number of alpha decay first based on the change in mass number since there is no change in mass number in beta decay, i.e., (238 – 206)4 = 8 (alpha decays).  After 8 alpha decays, atomic number should decrease by 8 x 2 = 16 which will change the atomic number to 92 – 16 = 76.  however, the atomic number in ²⁰⁶₈₂Pb is 82.  Therefore, 82 – 76 = 6 beta decays are needed to increase the atomic number from 76 to 82.