To determine the number of solutions to the given system of linear equations, we can analyze the equations:
- \(2x + y = 6\)
- \(4x + 2y = 8\)
First, let's simplify the second equation. Notice that the second equation is simply a multiple of the first equation:
From the first equation, if we multiply through by 2, we get:
\[ 4x + 2y = 12 \]
However, the second equation is:
\[ 4x + 2y = 8 \]
Since \(4x + 2y = 12\) is not equal to \(4x + 2y = 8\), this indicates that the two equations represent parallel lines that do not intersect.
Therefore, the system of equations has no solutions.
The correct answer is \(0\).