Solve by elimination.
\[
\begin{array}{r}
x-y=-4 \\
2 x+4 y=16
\end{array}
\]

Step 1 ：We are given the system of equations: \[\begin{array}{r} x-y=-4 \\ 2x+4y=16 \end{array}\]

Step 2 ：We can solve this system by elimination. The elimination method involves adding or subtracting the equations in order to eliminate one of the variables.

Step 3 ：In this case, we can multiply the first equation by 4 to match the coefficient of y in the second equation. This gives us a new equation: \[4x - 4y = -16\]

Step 4 ：We then add this new equation to the second equation to eliminate y: \[4x - 4y + 2x + 4y = -16 + 16\] which simplifies to \[6x = 0\]

Step 5 ：Solving for x, we find that \[x = 0\]

Step 6 ：Substituting x = 0 into the first equation, we can solve for y: \[0 - y = -4\] which simplifies to \[y = 4\]

Step 7 ：Final Answer: The solution to the system of equations is \(\boxed{x = 0, y = 4}\)