To solve the expression \(-6 + \frac{2\sqrt{5}}{-2}\), we start by simplifying the fraction.
1. Simplify \(\frac{2\sqrt{5}}{-2}\):
\[
\frac{2\sqrt{5}}{-2} = -\sqrt{5}
\]
2. Now substitute this back into the original expression:
\[
-6 - \sqrt{5}
\]
Thus, the final result is:
\[
-6 - \sqrt{5}
\]