It is important to know what α-particles are and what ß-particles are.
An α-particle is basically an Helium atom which contains 2 protons and 2 neutrons (i.e. mass number of 4 and atomic number of 2). Emission of an α-particle means that the atom’s mass number decreases by 4 and atomic number decreases by 2. Since 3 α-particles are emitted, mass number decreases by (3×4 =12) 12 and atomic number decrease by (2×3 = 6) 6.
So far, the current mass number of atom is 207 and atomic number is 80.
A ß-particle is an electron. So when a ß-particle is emitted, the atom loses an electron and the atomic number increases by 1.
Since 2 ß-particles are emitted, atomic number increases by 2 i.e. 80+2 = 82.
So, we have an atom which has a mass number of 207 and atomic number of 82. This corresponds to option C.