If your polygon is regular, then all the sides are the same length.
So you can write: 2x-4=4y-x=x+y.
Turning these into single equations,
2x-4=4y-x ----- (1)
2x-4=x+y ---- (2)
4y-x=x+y ----- (3)
from (3), 2x = 3y, or x = 3y/2
substituting for x = 3y/2 into (1),
3y - 4 = 4y - 3y/2
9y/2 - 4y = 4
y/2 = 4
y = 8
x = 12
These values for x and y give the three expressions for the length of a side as,
l = 2x-4 = 24 - 4 = 20
l = 4y-x = 32 - 12 = 20
l = x+y = 12 + 8 = 20
The same value for l is gotten each time which confiorms our solution, i.e.
x = 12 y = 8