1. **State the problem:** Multiply the binomials $4w + 2$ and $7w - 6$ using the area model or distributive property. 2. **Recall the distributive property (FOIL method):** $$ (a + b)(c + d) = ac + ad + bc + bd $$ where $a=4w$, $b=2$, $c=7w$, and $d=-6$. 3. **Multiply each term:** - First: $4w \times 7w = 28w^2$ - Outer: $4w \times (-6) = -24w$ - Inner: $2 \times 7w = 14w$ - Last: $2 \times (-6) = -12$ 4. **Combine like terms:** $$ 28w^2 - 24w + 14w - 12 $$ $$ 28w^2 - \cancel{24w} + \cancel{14w} - 12 $$ $$ 28w^2 - 10w - 12 $$ 5. **Final answer:** $$ \boxed{28w^2 - 10w - 12} $$ This is the product of the binomials $4w + 2$ and $7w - 6$.