1. **State the problem:** Multiply the polynomials using the box method: $$(5x + 4)(x - 2)$$ 2. **Set up the box:** The box has 2 rows and 2 columns. The top headers are $x$ and $-2$, the side headers are $5x$ and $4$. 3. **Multiply each pair:** - Top left cell: $5x \times x = 5x^2$ - Top right cell: $5x \times (-2) = -10x$ - Bottom left cell: $4 \times x = 4x$ - Bottom right cell: $4 \times (-2) = -8$ 4. **Fill the box:** \begin{tabular}{c|c|c} & $x$ & $-2$ \\ \hline $5x$ & $5x^2$ & $-10x$ \\ \hline $4$ & $4x$ & $-8$ \\ \end{tabular} 5. **Combine like terms:** $$5x^2 + (-10x) + 4x + (-8) = 5x^2 - 6x - 8$$ 6. **Final answer:** $$\boxed{5x^2 - 6x - 8}$$