1. **State the problem:** We need to find the value of $m$ such that the line $y = mx - 7$ is parallel to the line $2x + 3y = 6$. 2. **Recall the rule for parallel lines:** Two lines are parallel if and only if their slopes are equal. 3. **Find the slope of the given line $2x + 3y = 6$:** Rewrite in slope-intercept form $y = mx + b$: $$3y = -2x + 6$$ $$y = -\frac{2}{3}x + 2$$ So, the slope of this line is $-\frac{2}{3}$. 4. **Set the slope $m$ equal to $-\frac{2}{3}$:** Since the lines are parallel, $m = -\frac{2}{3}$. 5. **Answer:** The value of $m$ is $-\frac{2}{3}$. This corresponds to option C.