1. **Stating the problem:** Combine like terms in the expression $$(-2z - 3) + (4c + 6y) + (7 + 3c)$$. 2. **Formula and rules:** To combine like terms, add or subtract coefficients of terms with the same variable. Constants (numbers without variables) are combined separately. 3. **Step-by-step solution:** - Group like terms: $$(-2z) + (4c + 3c) + (6y) + (-3 + 7)$$ - Combine coefficients: $$4c + 3c = \cancel{4c} + \cancel{3c} = 7c$$ $$-3 + 7 = \cancel{-3} + \cancel{7} = 4$$ - Write the simplified expression: $$-2z + 7c + 6y + 4$$ 4. **Explanation:** We added coefficients of terms with the same variables and combined constants to simplify the expression. **Final answer:** $$-2z + 7c + 6y + 4$$