Four less than a number equals four times the sum of a number and 2. is this statement true for only one number, for all numbers, or for no numbers? explain your reasoning. also give the equation.

Alright lets interpret this first.
x - 4 = 4( x + 2 )

This question is basically asking you if it has infinite, none or only one solution.
To figure out no solutions you would need to find out if x = anything.

let's simplify first!
x - 4 = 4x + 8

Now once you remove all the parenthesis you can actually take out two options.
Infinite and No Solutions.

It is not infinite because in its simplest form they are still different.
It is not no solutions because it can still be done (they aren't impossible)

Example:
No solution -> (x+2)=(x+3)
Infinite -> (x+2)=(x+2)

Now back to the problem!
x - 4 = 4x + 8

Solve for x to find out what the solution is.

Do this first by taking out the x

-4 = 3x + 8

subtract the 8

-12 = 3x

finally divide by 3

-4 = x

Tada!

Hope this helps!