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

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 $\boxed{{\displaystyle x=0,y=4}}$