The length of a rectangular field is 4 m longer than its width.
if the perimeter is 56 m, what is the width of the field?

We know the perimeter is the sum of all sides. So lenght+length+width+width = 2length+2width.
Let's call the width x. If the length is 4m longer, then it's x+4.
We know the perimeter, so we can make an equation:
56=2x+2(x+4)
And solve from there:
56=2x+2x+8
56=4x+8
48=4x
48/4=x
x=12

The width, which is x, is 12 m. And the length, x+4, is 16 m.
You can check this is correct by calculating the perimeter using those values: 12+12+16+16=56.