1. The problem is to find the length of the hypotenuse $x$ in a right triangle where the legs are 6 and 8. 2. We use the Pythagorean Theorem which states: $$x^2 = a^2 + b^2$$ where $a$ and $b$ are the legs of the triangle. 3. Substitute the given values: $$x^2 = 6^2 + 8^2$$ 4. Calculate the squares: $$x^2 = 36 + 64$$ 5. Add the values: $$x^2 = 100$$ 6. Take the square root of both sides: $$x = \sqrt{100}$$ 7. Simplify the square root: $$x = 10$$ The length of the hypotenuse $x$ is 10.