Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust to counteract that change and restore a new equilibrium.
In the reaction you provided:
\[ \text{C(s)} + 2\text{H}_2(g) \rightleftharpoons \text{CH}_4(g) + 18 \text{ kcal} \]
if you remove \( \text{H}_2(g) \) from the system, the equilibrium will shift to the left in order to produce more \( \text{H}_2 \) to counteract the decrease in concentration.
Therefore, the effect of removing \( \text{H}_2 \) in this system would be to shift the equilibrium to the left, resulting in the formation of more reactants, \( \text{C} \) and \( \text{H}_2 \), and less product, \( \text{CH}_4 \).
The best answer to the question would be:
The equilibrium will shift to the left, producing more \(\text{H}_2\) and consuming \(\text{CH}_4\).