Answer
Seven $\alpha$ particles and four $\beta^{-}$ particles were emitted.
Work Step by Step
Only the $\alpha$ emissions decrease the mass number (by 4 each time, because of the loss of 2 protons and 2 neutrons). The mass number changes from 235 to 207, a decrease of 28. There must have been seven $\alpha$ particles emitted.
With each $\alpha$ particle emitted, the atomic number decreases by 2 (because of the loss of 2 protons and 2 neutrons). Considering only the alpha particles emitted, the atomic number would have decreased from 92 to 78.
When a $\beta^{-}$ particle is emitted, the atomic number rises by 1 (because of the emitted negative particle). Since the final atomic number is not 78, but 82, there must have been four $\beta^{-}$ particles emitted.