Question

[H₂S] = 0.10 M
[HCl] = 0.20 M $\Rightarrow$ [H⁺] = 0.2 M 
(1) H₂S $\rightleftharpoons$ HS^- + H⁺   K₁ = 1.0 $\times$ 10^-7
(2) HS $\rightleftharpoons$ S^2- + H⁺   K₂ = 1.2 $\times$ 10^-13
So,
H₂S $\rightleftharpoons$ S^2- + 2H⁺   K₁ $\times$ K₂
 = 1.2 $\times$10^-20
So, [S^2-] = $\frac{1.2\times {10}^{-20}\times \left[H_{2}S\right]}{[H^{+}{]}^2}$
$=\frac{1.2\times {10}^{-20}\times {10}^{-1}}{4\times {10}^{-2}}$
= 3 $\times$ 10^-20 M
All the [H⁺] will come from strong acid [HCl] only.