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If the width is W (unknown now), then the length is (3W - 6),
and your basic equation is
W + (3W-6) = 44/2, or
W + 3W - 6 = 22
4W = 22 + 6 = 28
W = 28/4 = 7.
ANSWER. The width is 7 feet. The length is 7*3-6 = 21-6 = 15 feet.
CHECK. The perimeter is 2W + 2L = 2*7 + 2*15 = 14 + 30 = 44 feet, which is PRECISELY CORRECT.
Solved.