If K_sp of ${\mathrm{Ag}}_2{\mathrm{CO}}_3$ is $8\times {10}^{-12}$, the molar solubility of   ${\mathrm{Ag}}_2{\mathrm{CO}}_3$ in 0.1 M ${\mathrm{AgNO}}_3$ solution is

$A{g}_{2}C{O}_3\rightleftarrows 2A{g}^{+}+C{O}_3^{2-} AgN{O}_3\to A{g}^{+}+N{O}_3^{-}$
S            (2S+0.1)  S     0.1         0.1       0.1
$K_{SP}={\left[A{g}^{+}\right]}^2\left[C{O}_3^{2-}\right]$
$8\times {10}^{-12}={(2S+0.1)}^2\left[S\right]$  $8\times {10}^{-12}={\left(0.1\right)}^2\left[S\right]$    [S<<0.1 So ‘2S’ is negligible]
$\mathrm{S}=\frac{8\times {10}^{-12}}{{10}^{-2}}=8\times {10}^{-10}$