1. **Stating the problem:** Simplify the expression $(6-\sqrt{7})(6-\sqrt{7})$. 2. **Formula used:** Use the distributive property (FOIL) for binomials: $$(a-b)(a-b) = a^2 - 2ab + b^2$$ 3. **Apply the formula:** Here, $a=6$ and $b=\sqrt{7}$. $$ (6-\sqrt{7})^2 = 6^2 - 2 \times 6 \times \sqrt{7} + (\sqrt{7})^2 $$ 4. **Calculate each term:** $$ 6^2 = 36 $$ $$ 2 \times 6 \times \sqrt{7} = 12\sqrt{7} $$ $$ (\sqrt{7})^2 = 7 $$ 5. **Combine all terms:** $$ 36 - 12\sqrt{7} + 7 $$ 6. **Simplify the constants:** $$ 36 + 7 = 43 $$ 7. **Final simplified expression:** $$ 43 - 12\sqrt{7} $$ This is the simplified form of the expression.