1. **State the problem:** Solve the equation $$12(2k + 11) = 12(2k + 12)$$ for $k$. 2. **Write the equation:** $$12(2k + 11) = 12(2k + 12)$$ 3. **Distribute 12 on both sides:** $$12 \times 2k + 12 \times 11 = 12 \times 2k + 12 \times 12$$ which simplifies to $$24k + 132 = 24k + 144$$ 4. **Subtract $24k$ from both sides:** $$\cancel{24k} + 132 = \cancel{24k} + 144$$ which simplifies to $$132 = 144$$ 5. **Analyze the result:** Since $132 \neq 144$, this means there is no value of $k$ that satisfies the equation. **Final answer:** There is no solution for $k$ because the equation simplifies to a false statement.