1. **State the problem:** We are given the complex number $$-2 - i\sqrt{3}$$ and it is expressed as $$x + iy$$ where $$x$$ and $$y$$ are real numbers. We need to find the value of $$y$$ when $$y = x$$. 2. **Identify the real and imaginary parts:** In the complex number $$-2 - i\sqrt{3}$$, the real part is $$-2$$ and the imaginary part is $$-\sqrt{3}$$. 3. **Match with $$x + iy$$:** Since $$x + iy = -2 - i\sqrt{3}$$, we have: $$x = -2$$ $$y = -\sqrt{3}$$ 4. **Given condition:** $$y = x$$, so we set: $$y = x$$ $$-\sqrt{3} = -2$$ 5. **Check equality:** The equation $$-\sqrt{3} = -2$$ is not true because $$\sqrt{3} \approx 1.732$$ which is not equal to 2. 6. **Conclusion:** There is no value of $$x$$ and $$y$$ such that $$y = x$$ for the given complex number $$-2 - i\sqrt{3}$$. The values are fixed as $$x = -2$$ and $$y = -\sqrt{3}$$, and they are not equal. **Final answer:** $$y \neq x$$ for the given complex number.