The first step was the combine the like terms; in this example he is subtracting the 3x on both sides of the =.
If you were to solve the equation it would look like this:
2x+6=3x-8
-3x -3x
-x+6=-8
-6 -6
-x=-14
/-1 /-1
x=14
Yes because when you subtract a number, you can also say that you added a negative. So if it dropped 23 degrees, then you also added -23 degrees