1. **State the problem:** Solve the equation $4(2x-1) = 3(x+2)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$4 \times 2x - 4 \times 1 = 3 \times x + 3 \times 2$$ which simplifies to $$8x - 4 = 3x + 6$$ 3. **Isolate the variable terms on one side:** Subtract $3x$ from both sides to get all $x$ terms on the left. $$8x - \cancel{3x} - 4 = \cancel{3x} + 6$$ which simplifies to $$5x - 4 = 6$$ 4. **Isolate the constant term:** Add $4$ to both sides to move constants to the right. $$5x - 4 + 4 = 6 + 4$$ which simplifies to $$5x = 10$$ 5. **Solve for $x$:** Divide both sides by $5$ to isolate $x$. $$\frac{5x}{\cancel{5}} = \frac{10}{\cancel{5}}$$ which simplifies to $$x = 2$$ **Final answer:** $x = 2$