If the perimeter of the rectangle to the right is 96 inches, find the value of x

You must have an illustration to give an idea what x represents. If not, then we can never find a way to answer this for you. However, for educational purposes, let me just suppose a figure for us to solve. The diagram is shown in the attached picture.

The rectangle has dimensions of 6 + x by x units, where x is the width and (6+x) is the length. If you are given the perimeter of the rectangle, then the working equation to be used is shown below.

Perimeter = 2L + 2W

Generally, perimeter is the sum of all sides of the figure. Since rectangle is defined to be made up of two sets of equal parallel sides called length and width, the perimeter is simplified to be that way. Substituting the values,

96 inches = 2(6+x) + 2x
96 = 12 + 2x + 2x
96 = 12 + 4x
4x = 96 - 12
4x = 84
x = 84/4
x = 21 inches