β⁻ emission is an emission of an electron from the parent atom while converting a neutron into a proton. Hence, the formed daughter nucleus has the same number of mass but the atomic number is higher by 1 and number of neutrons is lower by one than the parent atom.
After a β⁻ emission of ¹⁰⁶Ru, the formed daughter nucleus should have 106 as mass number but (44 + 1) = 45 as the atomic number.
Hence the daughter nucleus is Rh (Rhodium) which has 45 protons (atomic number).