There are five steps to solving simple algebraic equations

1. Clear any fractions by multiplying all the terms on both sides of the equation by the denominators
2. Remove all parentheses
3. Transpose all of the terms containing the unknown variable to one side of the equation and all known numbers or variables on the other side of the equation
4. Combine like terms on each side of the equation
5. Divide both sides by whatever coefficient is in front of the unknown variable.

For our equation since we don't have fractions or parenthesis, we can begin with step 3 and using a rule of algebra of performing the inverse of a function to move it from one side of the equation to the other.  In order to move  +6x   to the left side of the equation, we will subtract  6x from both sides.  Likewise, to move the  -4x  to the left side, we will add 4x to both sides.  The same rule applies to the known variables.

8x + 7 - 3x = 6x + 19 - 4x  now becomes
8x - 3x - 6x + 4x = 19 - 7

Next, reduce the complexity of the equation by combining like terms on each side of the equation

3x = 12

Lastly, remove the coefficient from the unknown term, again using the rule of performing the inverse of a function.  The inverse of 3 is 1/3, so multiply both sides of the equation by 1/3.  Or to state it another way, divide both sides by 3.

x = 4.

First combine terms with x's in them and combine the others to get:

5x + 7 = 2x + 19

Then subtract 2x from both sides and subtract 7 from both sides to get:

3x = 12