Answer
See explanation.
Work Step by Step
$N_{210} $ = The amount of Pb Nuclei that changes because of two decay which is
1. Decay from $^{226}Ra $ into $^{210} Pb$ (rate $R_{226} =\lambda_{226} R_{226}$)
2. Decay from $^{210}Pb $ into $^{206} Pb$ (rate $R_{210} = \lambda_{210} R_{210})$
Since the first decay causes $N_{210}$ to increase and second decay causes it to decrease, the equation becomes
$\frac{dN_{210}}{dt} = R_{226} - R_{210}$
$\frac{dN_{210}}{dt} = \lambda_{226} R_{226} - \lambda_{210} R_{210} $
