1. **State the problem:** We need to find the value of $r$ such that $(y+2)$ is a factor of the polynomial $3y^2 - 4ry - 4r^2$. 2. **Recall the factor theorem:** If $(y+2)$ is a factor of the polynomial, then substituting $y = -2$ into the polynomial should give zero. 3. **Apply the factor theorem:** Substitute $y = -2$ into $3y^2 - 4ry - 4r^2$: $$3(-2)^2 - 4r(-2) - 4r^2 = 0$$ 4. **Simplify the expression:** $$3 \times 4 + 8r - 4r^2 = 0$$ $$12 + 8r - 4r^2 = 0$$ 5. **Rewrite as a quadratic in $r$:** $$-4r^2 + 8r + 12 = 0$$ 6. **Divide entire equation by -4 to simplify:** $$r^2 - 2r - 3 = 0$$ 7. **Factor the quadratic:** $$(r - 3)(r + 1) = 0$$ 8. **Solve for $r$:** $$r = 3 \quad \text{or} \quad r = -1$$ **Final answer:** The values of $r$ are $3$ or $-1$.