1. **State the problem:** We are given the linear equation $3x - 2y + 6 = 0$ and the point $(-3, -3)$. We want to check if the point lies on the line. 2. **Recall the rule:** A point $(x_0, y_0)$ lies on the line given by $Ax + By + C = 0$ if substituting $x = x_0$ and $y = y_0$ satisfies the equation. 3. **Substitute the point into the equation:** $$3(-3) - 2(-3) + 6 = -9 + 6 + 6$$ 4. **Simplify the expression:** $$-9 + 6 + 6 = 3$$ 5. **Interpret the result:** Since the left side equals $3$ and not $0$, the point $(-3, -3)$ does not satisfy the equation. **Final answer:** The point $(-3, -3)$ does not lie on the line $3x - 2y + 6 = 0$.