$\begin{aligned} \text { Vol. of metal }=\frac{\text { Mass }}{\text { Density }}=\frac{38.6 \mathrm{~g}}{19.3 \mathrm{~g} \mathrm{~cm}^{-3}} &=2 \mathrm{~cm}^{3} \\ \text { No. of unit cells in } 38.6 \mathrm{~g} \text { of noble metal } &=\frac{\text { Total vol. of metal }}{\text { Vol. of one unit cell }} \\ &=\frac{2 \mathrm{~cm}^{3}}{6.18 \times 10^{-23} \mathrm{~cm}^{3}}=3.236 \times 10^{22} \end{aligned}$