The given system of linear equations is:
2x + y = 6 ...(1)
4x + 2y = 8 ...(2)
We can simplify equation (2) by dividing both sides by 2:
2x + y = 4 ...(3)
Now, if we compare equations (1) and (3), we can see that they represent the same line. The two equations have the same slopes and y-intercepts.
This means that the two equations are dependent, and they represent the same line. Therefore, they have infinitely many solutions.
So, the correct answer is: infinite.