The provided reaction is:

$$\frac{1}{2} \mathrm{H}_{2}(\mathrm{~g})+\mathrm{AgCl}(\mathrm{s}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{Ag}(\mathrm{s})$$

This reaction involves the following half-reactions:

1. Oxidation of hydrogen gas to H+ ions: $$\frac{1}{2} \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq}) + e^-$$


2. Reduction of AgCl to Ag: $$\mathrm{AgCl}(\mathrm{s}) + e^- \rightleftharpoons \mathrm{Ag}(\mathrm{s}) + \mathrm{Cl}^{-}(\mathrm{aq})$$

Looking at the options provided:

Option A: Doesn't involve H₂ gas, so it can't be correct.

Option B: This includes the necessary elements - H₂, AgCl, and Ag.

Option C: Doesn't involve AgCl, so it can't be correct.

Option D: Also includes the necessary elements - H₂, AgCl, and Ag.

However, looking closely, we can see that Option B represents the galvanic cell for this reaction. The reaction requires the oxidation of H₂ to H⁺, which occurs at the anode. The reaction also requires the reduction of AgCl to Ag and Cl-, which occurs at the cathode.

In Option B, the anode (on the left) is where H₂ is being oxidized to H⁺. The cathode (on the right) is where AgCl is reduced to Ag and Cl^-. The salt bridge or ion exchange component is HCl, which allows for the flow of ions to balance charge in the cell.

Therefore, the reaction occurs in the galvanic cell represented by Option B.