The length of a rectangular lot is 6 feet less than 4 times its width. its area is 256 sqaure feet.

The formula for the area of a rectangle is length times width, or A=l·w

The Area A=256 
The width is w
The lenght is given as 6 feet less than 4 times its width, or in math language this is l=4w-6

Let's go back to the formula
A=l·w ⇒ 256=(4w-6)·w
simplify ⇒ 256=4w²-6w
put everything on the same side and set the equation equal to zero 
⇒ 4w²-6w-256=0
Solve for w using quadratic formula

You are going to get two answers after using the quadratic formula: one positive and one negative. Just remember it doesn't make sense to get a negative answer if we are talking about width, so use the positive answer only

w≈8.7851 units

Width is x
Length is 4x-6
total area=256
256=length*width
256=x*(4x-6)
256=4x^2-6x
256=4x^2-6x
0=4x^2-6x-256
You can solve the equation-
you should get (3+-√1033)/4- Hope this helps