The problem to solve is:

2 (x + 4) + 4 (x - 6)=80

First, let's work on the left hand side of your equation, the 2 (x + 4) + 4 (x - 6)
This means, for instance, to see if it can be simplified at all.
x+4 evaluates to x+4

Multiply 2 by x+4

we multiply 2 by each term in x+4 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 4

1

2 × 4 = 8

2*(x+4) evaluates to 2x+8

x-6 evaluates to x-6

Multiply 4 by x-6

we multiply 4 by each term in x-6 term by term.

This is the distributive property of multiplication.

Multiply 4 and x

Multiply 1 and x

The x just gets copied along.

x

4 × x = 4x

Multiply 4 and -6

1

4 × -6 = -24

4*(x-6) evaluates to 4x-24

To add the polynomials 2x+8 and 4x-24 we try to add or combine terms in one polynomialwith any like terms in the other polynomial.

2x + 4x = 6x

8 + -24 = -16 The answer is 6x-16

2*(x+4)+4*(x-6) evaluates to 6x-16

So, all-in-all, the left hand side of your equation can be written as: 6x-16

Now, let's work on the right hand side of your equation, the 80
The right hand side of your equation can be written as: 80
So with these (any) simplifications, the equation we'll set out to solve is:
6x-16 = 80

Move the -16 to the right hand side by adding 16 to both sides, like this:

To the left hand side:
-16 + 16 = 0 The answer is 6x

To the right hand side:
80 + 16 = 96 The answer is 96

6x = 96
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 6 like this:

To divide x by 1

The x just gets copied along in the numerator. The answer is x

6x ÷ 6 = x

96 ÷ 6 = 16

The solution to your equation is:
x = 16