1. **State the problem:** We need to find the radius of a circle given a point $P(-\sqrt{6}, 2)$ on the circle. 2. **Formula used:** The radius $r$ of a circle with center at the origin $(0,0)$ and a point $P(x,y)$ on the circle is given by the distance formula: $$r = \sqrt{x^2 + y^2}$$ 3. **Apply the formula:** Substitute $x = -\sqrt{6}$ and $y = 2$: $$r = \sqrt{(-\sqrt{6})^2 + 2^2}$$ 4. **Simplify inside the square root:** $$r = \sqrt{6 + 4}$$ 5. **Add the terms:** $$r = \sqrt{10}$$ 6. **Final answer:** The radius of the circle is $$\boxed{\sqrt{10}}$$