4x – 9 = 2x + 15 can someone explain the system used to answer this question

The system is comprised of two processes
that go on at the same time:

       #1). Do what ever you want to, to get 'x'
               on one side of the equation, and
               everything else on the other side.
       #2). Whatever you do to one side of the equation,
               you must immediately do the same thing to the
               other side.

That's the system.

Here's how it works:  (I can't believe you're in high school math
and you've never seen, studied, or practiced this before.)

You said that                               4x - 9  =  2x + 15                   
and you need to find
what 'x' is.

Subtract  2x  from each side:    2x - 9  =           15

Add  9  to each side:                 2x        =            24

Divide each side by  2 :              x        =             12 .  

The year before the 10s so it was like when caveman were alive