In the given equilibrium reaction:
\[ \text{H}_2 + \text{I}_2 \rightleftharpoons 2 \text{HI} \]
If more hydrogen gas (H2) is added to the system, according to Le Chatelier's principle, the equilibrium will shift to counteract the change. In this case, the addition of hydrogen will shift the equilibrium to the right, towards the production of more hydrogen iodide (HI).
Therefore, the correct response would be:
The amount of hydrogen iodide (HI) increases.