1. **State the problem:** Simplify the expression $$(4-\sqrt{10})(4+\sqrt{10})$$. 2. **Formula used:** This is a product of conjugates, which follows the formula $$(a-b)(a+b) = a^2 - b^2$$. 3. **Apply the formula:** Here, $a=4$ and $b=\sqrt{10}$. 4. **Calculate each square:** $$a^2 = 4^2 = 16$$ $$b^2 = (\sqrt{10})^2 = 10$$ 5. **Subtract the squares:** $$16 - 10 = 6$$ 6. **Final answer:** The simplified form of $$(4-\sqrt{10})(4+\sqrt{10})$$ is $$6$$.