Solution: Cross-multiply: $ 2(3y - 1) = 4(y + 7) $. Expand: $ 6y - 2 = 4y + 28 $. Subtract $ 4y $: $ 2y - 2 = 28 $. Add 2: $ 2y = 30 $. Divide by 2: $ y = 15 $. Final answer: $ \boxed{15} $.

["How to Solve Linear Equations Using Cross-Multiplication: A Step-by-Step Example", "Solving linear equations is a fundamental skill in algebra, essential for students, educators, and anyone working with quantitative reasoning. One powerful technique involves cross-multiplication and simplification to isolate the variable. This article breaks down the solution process for a classic equation: $ 2(3y - 1) = 4(y + 7) $, using clear, step-by-step algebra.", "---", "### Understanding Cross-Multiplication Boundaries", "Although the term “cross-multiply” is often associated with proportions, when dealing with equations containing parentheses and coefficients, similar principles apply—simplifying both sides until variables and constants are neatly aligned. In this example, we expand brackets and combine like terms to solve for $ y $ efficiently.", "---", "### Step 1: Expand Both Sides", "Start with the original equation:\n$$\n2(3y - 1) = 4(y + 7)\n$$", "Apply the distributive property (cross-multiplying effectively here):\n$$\n2 \cdot 3y - 2 \cdot 1 = 4 \cdot y + 4 \cdot 7\n\Rightarrow 6y - 2 = 4y + 28\n$$", "This matches the expanded form given:\n$$\n6y - 2 = 4y + 28\n$$", "---", "### Step 2: Subtract $ 4y $ from Both Sides", "To isolate the variable terms on one side, subtract $ 4y $ from both sides:\n$$\n6y - 4y - 2 = 4y - 4y + 28\n\Rightarrow 2y - 2 = 28\n$$", "This simplifies the equation by consolidating $ y $-terms, bringing all constant terms to the other side.", "---", "### Step 3: Add 2 to Both Sides", "Now eliminate the constant on the left by adding 2 to both sides:\n$$\n2y - 2 + 2 = 28 + 2\n\Rightarrow 2y = 30\n$$", "---", "### Step 4: Divide by 2 to Solve for $ y $", "Finally, divide both sides by 2 to isolate $ y $:\n$$\n\frac{2y}{2} = \frac{30}{2}\n\Rightarrow y = 15\n$$", "---", "### Final Answer", "The solution to the equation $ 2(3y - 1) = 4(y + 7) $ is\n$$\n\boxed{15}\n$$", "---", "### Why This Method Works", "By expanding expressions and combining like terms, we transform complex equations into simpler linear forms—applying foundational algebraic principles efficiently. Whether learning math or solving real-world problems, mastering cross-multiplication-style simplification builds confidence and clarity in equation solving.", "For quicker verification, always substitute $ y = 15 $ back into the original equation to confirm both sides are equal—adding a layer of accuracy and understanding.", "---", "Key Takeaways:\n- Always expand both sides fully before combining terms.\n- Use elimination and division to isolate variables.\n- Verify your solution by substitution.\n- This method generalizes to all linear equations with parentheses and coefficients.", "Get comfortable with cross-multiplying and simplifying—your algebra toolkit just got stronger!"]