To determine the number of solutions to the system of equations given by:
- \( 2x + y = 6 \)
- \( 4x + 2y = 8 \)
we can start by analyzing the second equation. We can simplify it:
\[ 4x + 2y = 8 \]
Dividing every term by 2, we get:
\[ 2x + y = 4 \]
Now, we have two equations:
- \( 2x + y = 6 \)
- \( 2x + y = 4 \)
Next, we can see that both left-hand sides of these equations are equal (\(2x + y\)), but the right-hand sides differ (6 and 4). Since \(2x + y\) cannot equal both 6 and 4 at the same time, this system of equations has no solutions.
Thus, the number of solutions to this system is:
\[ \boxed{0} \]