1. **State the problem:** We are given a line $p$ with slope $m = -\frac{5}{3}$ and an $x$-intercept at $(-6, 0)$. We need to find the $y$-coordinate of the $y$-intercept of this line. 2. **Recall the slope-intercept form:** The equation of a line can be written as $$y = mx + b$$ where $m$ is the slope and $b$ is the $y$-intercept (the $y$-coordinate when $x=0$). 3. **Use the given information:** We know $m = -\frac{5}{3}$ and the line passes through $(-6, 0)$. 4. **Substitute the point into the equation:** Plug $x = -6$ and $y = 0$ into $$y = mx + b$$ to find $b$: $$0 = -\frac{5}{3} \times (-6) + b$$ 5. **Simplify:** $$0 = 10 + b$$ 6. **Solve for $b$:** $$b = -10$$ 7. **Interpretation:** The $y$-intercept is at $(0, -10)$, so the $y$-coordinate of the $y$-intercept is $-10$. **Final answer:** The $y$-coordinate of the $y$-intercept of line $p$ is $\boxed{-10}$.