The length of a rectangle is one unit shorter than one-sixth of the width, x.

which expression represents the perimeter of the rectangle?

To answer this question, you need to know the formula for calculating the perimeter of a rectangle and translating the description into the formula. The description formula should be:
width = x
length - 1 = 1/6 x
length= 1/6 x +1 

Then adding them to perimeter formula you will get
perimeter= length * width
perimeter= 1/6x+ 1 * x= 1/6x^2 + x