There is something wrong with the first equation.
The first step is collect like terms, on the Right Hand Side, you have 4x and -2x, (if you have 4 apples and give away 2, how many apples you got?)
5+2x = 2x+6
Once you got to this point would be to move the x to the same side of the balance, to do that, you can take away 2 'apples' if you also take away 2 'apples' on the other side of the balance.
5+2x - 2x = 2x-2x+6
This is where you see that this equation is not solvable, as you will have: 5=6 what is an absurd
Using the same method on the second one, collecting like terms, we have
12x -3 = 6x
We want to have all the terms with the 'x' on the same side and the rest on the other.
Starting with the 'x's, we will subtract 6x on both sides (to keep the balance)
12x-6x -3 = 6x-6x
6x-3=0
The '3' on the left is subtracting, to get rid of it, we will have to do the opposite of what is doing. We will add 3 on both sides to keep the balance
6x-3+3=3
6x=3
Finally, 6x is the same as 6 times x. To move the 6 to the other side, we do again the opposite. Dividing by 6 on both sides:
6x/6=3/6
x=1/2