To determine the number of solutions to the given system of linear equations, we will start by rearranging both equations and checking if they are equivalent.
The first equation is:
\[ -2y = 4x + 8 \]
We can rearrange it to the standard form \(Ax + By = C\). Dividing both sides by -2:
\[ y = -2x - 4 \]
The second equation is already given as:
\[ y = -2x - 4 \]
Now we can see that both equations are the same:
\[ y = -2x - 4 \] \[ y = -2x - 4 \]
Since both equations represent the same line, there are infinitely many solutions for the system. This means that every point on the line \(y = -2x - 4\) is a solution to the system.
Therefore, the number of solutions to the system of linear equations is:
\[ \text{Infinitely many solutions} \]