Solve the system of equations. If the system has no solution, say that it is inconsistent. \[ \left\{\begin{array}{r} x+2 y=4 \\ 2 x+4 y=8 \end{array}\right. \]

Step 1 ：The system of equations is a linear system. The second equation is a multiple of the first one. This means that the two equations are dependent and represent the same line.

Step 2 ：Therefore, there are infinitely many solutions to this system.

Step 3 ：The solution to the system of equations is a family of points \((x, y)\) such that \(x = 4 - 2y\).

Step 4 ：This means that for any real number \(y\), there is a corresponding \(x\) that makes both equations true.

Step 5 ：\(\boxed{\text{The system of equations has infinitely many solutions.}}\)