1. **Stating the problem:** Simplify the expression $3 - 2\sqrt{5} + 6\sqrt{5}$ and find its equivalent form. 2. **Combine like terms:** The terms $-2\sqrt{5}$ and $6\sqrt{5}$ are like terms because they both contain $\sqrt{5}$. 3. **Add the coefficients of $\sqrt{5}$:** $$-2 + 6 = 4$$ 4. **Rewrite the expression:** $$3 - 2\sqrt{5} + 6\sqrt{5} = 3 + 4\sqrt{5}$$ 5. **Final answer:** The expression is equivalent to $3 + 4\sqrt{5}$.