To solve the expression \(-6 + 2\sqrt{5} \div -2\), we first need to clarify the order of operations and handle the division.
1. **Handle the division first**:
\[
2\sqrt{5} \div -2 = \frac{2\sqrt{5}}{-2} = -\sqrt{5}
\]
2. **Substituting back into the expression**:
\[
-6 + (-\sqrt{5}) = -6 - \sqrt{5}
\]
Therefore, the final result is:
\[
-6 - \sqrt{5}
\]