In a radioactive decay chain, _ 90 ^ 232 Th nucleus decays to _ 82...

{}_{90}^{232}Th$is converting into${}_{82}^{212}Pb$<br />Change in mass number \left(A\right) = 232 - 212 = 20$

Mass number of an $\alpha$ particle $= 4$
$∴$ No of $\alpha\text{particle} = \dfrac{20}{4} = 5$
Due to $5\alpha$ particle, $Z$ will change by $10$ unit.
Since given change is $8$, therefore no. of ${\beta}^{-}$ particle is $2$.