1. **State the problem:** Rewrite the expression by factoring out $ (y - 6) $ from the expression $$5 y^2 (y - 6) - 3 (y - 6)$$. 2. **Identify the common factor:** Both terms contain the factor $ (y - 6) $, so we can factor it out. 3. **Factor out $ (y - 6) $:** $$5 y^2 (y - 6) - 3 (y - 6) = (y - 6)(5 y^2) - (y - 6)(3)$$ $$= (y - 6)(5 y^2 - 3)$$ 4. **Final answer:** The expression factored by $ (y - 6) $ is $$\boxed{(y - 6)(5 y^2 - 3)}$$.