let

l = the length of the rectangular filter, l>0

w = the width of the rectangular filter, w>0

the length of a rectangular air filter that is 4 inches less than twice the width

l = 2w - 4

the area is 286 square inches

l*w = 286

plug l = 2w - 4 into the last equation

(2w - 4)*w = 286

by solving we find

w = 13 in

click here to see the step by step solution of the equation

l = 2*13 - 4

l = 22 in

the length is 22 inches while the width is 13 inches.