To determine the number of solutions to the system of equations given by:
- \( 2x + y = 6 \)
- \( 4x + 2y = 8 \)
We can manipulate the second equation. Notice that the second equation can be simplified:
\[ 4x + 2y = 8 \implies 2(2x + y) = 8 \implies 2x + y = 4 \]
Now we have the two equations:
- \( 2x + y = 6 \)
- \( 2x + y = 4 \)
These two equations describe two different lines. The first line has a y-intercept of 6, and the second has a y-intercept of 4. Since they have the same slope but different y-intercepts, the lines are parallel and will never intersect.
Since the lines do not intersect, there are no solutions to this system of equations.
Thus, the number of solutions is \( \boxed{0} \).