The problem to solve is:

4x+2(4-2(x+2))=2x-4

First, let's work on the left hand side of your equation, the 4x+2(4-2(x+2))
This means, for instance, to see if it can be simplified at all.
Multiply x and 4

Multiply x and 1

The x just gets copied along.

The answer is x

x

4*x evaluates to 4x

x+2 evaluates to x+2

Multiply 2 by x+2

we multiply 2 by each term in x+2 term by term.

This is the distributive property of multiplication.

Multiply 2 and x

Multiply 1 and x

The x just gets copied along.

x

2 × x = 2x

Multiply 2 and 2

1

2 × 2 = 4

2*(x+2) evaluates to 2x+4

4 - 4 = 0

The answer is -2x

4-2*(x+2) evaluates to -2x

Multiply 2 and -2x

Multiply 1 and x

The x just gets copied along.

x

2*(4-2*(x+2)) evaluates to -4x

4*x+2*(4-2*(x+2)) evaluates to 0x

So, all-in-all, the left hand side of your equation can be written as: 0x


Now, let's work on the right hand side of your equation, the 2x-4
Multiply x and 2

Multiply x and 1

The x just gets copied along.

The answer is x

x

2*x evaluates to 2x

2*x-4 evaluates to 2x-4

The right hand side of your equation can be written as: 2x-4


So with these (any) simplifications, the equation we'll set out to solve is:
0x = 2x-4

Move the 2x to the left hand side by subtracting 2x from both sides, like this:
From the left hand side:
0x - 2x = -2x

The answer is -2x

From the right hand side:
2x - 2x = 0

The answer is -4


Now, the equation reads:
-2x = -4
To isolate the x, we have to divide both sides of the equation by the other variables
around the x on the left side of the equation.


The last step is to divide both sides of the equation by -2 like this:

To divide x by 1

The x just gets copied along in the numerator.

The answer is x

-2x ÷ -2 = x

-4 ÷ -2 = 2

The solution to your equation is:
x = 2