You can use variables in place of length and width and use the formula for perimeter of the rectangle to get an equation.
The perimeter of the considered frame will be greater than 156 when we will have [tex]x > 36[/tex] inches
How to find the value of unknown variable x?
It depends on the context.
Sometimes we can and sometimes we cannot.
For this case, let we take width of the picture frame as of [tex]x[/tex] inches
Then, as said in the problem, the length of the frame is 6 inches more than width which is [tex]x + 6[/tex] inches.
Using the formula for perimeter of a rectangle, we get
[tex]Perimeter = 2 ( length + width)\\Perimeter = 2(x + 6 + x) = 2(2x + 6) \text{\:\:\:(Like terms coefficients added together)}\\Perimeter = 4x + 12[/tex](in inches)
(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2 \times x = 2x[/tex])
Now, when perimeter is greater than 156 inches, we get the inequality as
[tex]Perimeter > 156\\4x + 12 > 156\\\\\text{Subtracting 12 from both the sides}\\\\4x > 144\\\\\text{Dividing both the sides by 4}\\\\x > 36[/tex]
(we didn't write inches in equation since it was known from the context that all measurements are in equations and usually we don't use units or such things in equation and write it separately)
Thus, for any value of [tex]x > 36[/tex] inches, the perimeter of the frame will come out to be bigger than 156 inches
Learn more here about inequalities here:
https://brainly.com/question/11901702
