First, calculate the decay constant $k$ using the half-life $T_{1/2} = 5600 \text{ years}$: $$ \begin{aligned} k &= \frac{\ln 2}{T_{1/2}} \\ &= \frac{0.693}{5600 \text{ yr}} \\ &= 1.2375 \times 10^{-4} \text{ yr}^{-1} \end{aligned} $$ Now, use the first-order integrated rate equation to find the age $t$: $$ \begin{aligned} t &= \frac{1}{k} \ln\left(\frac{C_0}{C_t}\right) \end{aligned} $$ Given $C_0 = 20 \text{ cpm g}^{-1}$ and $C_t = 12 \text{ cpm g}^{-1}$: $$ \begin{aligned} t &= \frac{1}{1.2375 \times 10^{-4}} \ln\left(\frac{20}{12}\right) \\ &= \frac{1}{1.2375 \times 10^{-4}} \ln(1.6667) \\ &= \frac{0.5108}{1.2375 \times 10^{-4}} \\ &= 4127.88 \text{ years} \end{aligned} $$ The age of the doll is approximately $4127.88$ years.