1. The problem asks us to estimate the limit $$\lim_{x \to 4} g(x)$$ using the given table of values for the function $g$ near $x=4$. 2. The limit $$\lim_{x \to a} f(x)$$ is the value that $f(x)$ approaches as $x$ gets arbitrarily close to $a$ from both sides. 3. From the table, as $x$ approaches 4 from the left (3.9, 3.99, 3.999), $g(x)$ values are 11.21, 11.92, 11.99, which are getting closer to 12. 4. As $x$ approaches 4 from the right (4.001, 4.01, 4.1), $g(x)$ values are 12.01, 12.08, 12.81, also approaching 12. 5. Since the values of $g(x)$ from both sides approach 12, a reasonable estimate for the limit is 12. 6. Therefore, the answer is (C) 12.