1. Stated problem: Simplify the expression $$4(11x + 4y) + 5(2x + 4y)$$ and find which given option is equivalent. 2. Use distributive property: $$a(b + c) = ab + ac$$. 3. Expand each term: $$4(11x + 4y) = 4 \times 11x + 4 \times 4y = 44x + 16y$$ $$5(2x + 4y) = 5 \times 2x + 5 \times 4y = 10x + 20y$$ 4. Add the expanded terms: $$44x + 16y + 10x + 20y = (44x + 10x) + (16y + 20y) = 54x + 36y$$ 5. Check each option by expanding: A) $$12(4x + 4y) = 48x + 48y$$ (not equal) B) $$18(3x + 4y) = 54x + 72y$$ (not equal) C) $$9(6x + 4y) = 54x + 36y$$ (equal) D) $$6(9x - 6y) = 54x - 36y$$ (not equal) 6. Conclusion: Option C is equivalent to the original expression. Final answer: C