1. **State the problem:** We have a quadratic function $$y = 3a x^2 - q$$ and it passes through the point $(-1, 6)$. We need to find the coordinates of another point on the parabola. 2. **Use the given point to find a relationship:** Substitute $x = -1$ and $y = 6$ into the equation: $$6 = 3a (-1)^2 - q$$ $$6 = 3a - q$$ 3. **Express $q$ in terms of $a$:** $$q = 3a - 6$$ 4. **Rewrite the function using $q$:** $$y = 3a x^2 - (3a - 6) = 3a x^2 - 3a + 6$$ 5. **Choose another $x$ value to find a new point:** For example, let $x = 0$: $$y = 3a (0)^2 - 3a + 6 = -3a + 6$$ 6. **Coordinates of the new point:** $$(0, -3a + 6)$$ Since $a$ is not given, the new point depends on $a$. However, this is a valid point on the parabola for any $a$. **Final answer:** Another point on the parabola is $\boxed{(0, -3a + 6)}$.