1. **State the problem:** Multiply the binomials $(x + 2)(3x + 3)$ using the area model. 2. **Formula and rules:** To multiply two binomials, use the distributive property (FOIL method): $$ (a + b)(c + d) = ac + ad + bc + bd $$ Each term in the first binomial multiplies each term in the second. 3. **Apply the formula:** $$ (x + 2)(3x + 3) = x \cdot 3x + x \cdot 3 + 2 \cdot 3x + 2 \cdot 3 $$ 4. **Calculate each product:** $$ x \cdot 3x = 3x^2 $$ $$ x \cdot 3 = 3x $$ $$ 2 \cdot 3x = 6x $$ $$ 2 \cdot 3 = 6 $$ 5. **Combine like terms:** $$ 3x^2 + 3x + 6x + 6 = 3x^2 + (3x + 6x) + 6 = 3x^2 + 9x + 6 $$ 6. **Interpretation with area model:** - The $3x^2$ corresponds to the three $x^2$ tiles. - The $9x$ corresponds to the nine $x$ tiles. - The $6$ corresponds to the six unit squares. **Final answer:** $$ \boxed{3x^2 + 9x + 6} $$