Create a system of equation based on the problem
An expression for "the length is 6 yards longer than double the width"
⇒ l = 2w + 6 (first equation)
An expression for "perimeter is 282 yards"
⇒ 2l + 2w = 282 (second equation)
Work on the system of equation by substitution method
Substitute (2w + 6) as l, to the second equation
2l + 2w = 282
2(2w + 6) + 2w = 282
4w + 12 + 2w = 282
6w + 12 = 282
6w = 282 - 12
6w = 270
w = 270/6
w = 45
The dimension of the field is 45 yards
Substitute the value of w, that is 45, to the first equation to find the value of l
l = 2w + 6
l = 2(45) + 6
l = 90 + 6
l = 96
The length of the field is 96 yards