1. **Stating the problem:** We have a right triangle with legs labeled $a$ and $b$, and hypotenuse $c$. Given values are $b=4$, $a=6$, and we want to find $c$ using the Pythagorean theorem. 2. **Formula used:** The Pythagorean theorem states: $$c^2 = a^2 + b^2$$ This applies only to right triangles, where $c$ is the side opposite the right angle. 3. **Substitute known values:** $$c^2 = 6^2 + 4^2$$ 4. **Calculate squares:** $$c^2 = 36 + 16$$ 5. **Add the squares:** $$c^2 = 52$$ 6. **Find $c$ by taking the square root:** $$c = \sqrt{52}$$ 7. **Simplify the square root:** $$c = \sqrt{4 \times 13} = \sqrt{4} \times \sqrt{13} = 2\sqrt{13}$$ **Final answer:** $$c = 2\sqrt{13}$$