If a species ${}^{b}_{a}X$ emits firstly a positron, then two $\alpha$ and two $\beta$ particles and at last one $\alpha$ is also emitted and finally it converts into stable species ${}^{c}_{d}Y$, so correct relation will be : -

Here b is the mass number and a is the atomic number of X; c and d are the mass number and atomic number of Y.
Effect of each emission: positron ($\beta^+$): A unchanged, Z decreases by 1. $\alpha$: A decreases by 4, Z decreases by 2. $\beta^-$: A unchanged, Z increases by 1.
Change in mass number: three $\alpha$ particles in total, so $c = b - 3 \times 4 = b - 12$.
Change in atomic number: $-1$ (positron) $- 2 \times 2$ (two $\alpha$) $+ 2 \times 1$ (two $\beta$) $- 2$ (last $\alpha$) $= -5$, so $d = a - 5$.
So the correct relation is c = b – 12 and d = a – 5.