1. **State the problem:** We need to find the value of $x$ for a linear function passing through points $(x, 2)$ and $(-4, 6)$ with slope $m=3$. 2. **Recall the slope formula:** The slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Substitute the known values:** Here, $m=3$, $(x_1, y_1) = (x, 2)$, and $(x_2, y_2) = (-4, 6)$, so $$3 = \frac{6 - 2}{-4 - x} = \frac{4}{-4 - x}$$ 4. **Solve for $x$:** Multiply both sides by $-4 - x$: $$3(-4 - x) = 4$$ $$-12 - 3x = 4$$ Add 12 to both sides: $$-3x = 16$$ Divide both sides by $-3$: $$x = \frac{16}{-3} = -\frac{16}{3}$$ 5. **Final answer:** The value of $x$ is $-\frac{16}{3}$. **Answer choice:** c. $-\frac{16}{3}$