Math..linear equation..PLEASE HELP :(

I am getting so frustrated and need help. I have tried several different sources and can't seem to understand this: Solve the system using the elimination method:

2x-y=13
6x+4y=4
in the book it stated if you multiply the top equation by -3, you'll get -6x+3y= -39

I don't understand where the -3 came from and how do you know what
to multiply by when dealing with equations like this.
It also stated that you could have multiplied the top equation by 6 and
the bottom equation by -2 which I did and i got a totally different answer
which was y= -35, the answer should have been (4,5). Im not looking for the answer but a
better understanding. please help and if you can answer please do so in a way that I
can understand. I get really confused quick and its easy for me to get lost if it is not
translated and broken down step by step, literally. Thanks in advance. I feel so hopeless
and overwhelmed by this as if I am never going to understand the elimination method:(

What you're trying to do is eliminate one of the unknowns.
-3(2x - y) = -3(13)
This is the same equation just multiplying both sides by -3.
And now you can see that both equations have 6x in it which can be eliminated by addition.
So from the first equation, you get
-6x + 3y = -39
6x + 4y = 4
Adding these together, you get
7y = -35
y = - 5
Now you have the value of one of the unknowns (y)
Plug that number into either of the original equations to solve for x
2x -(-5) = 13
2x + 5 = 13
2x = 8
x = 4
So x = 4, y = -5
If you use these values in the second equation, you'll see that they also are answers for it.
6(4) + 4(-5) = 4
24 - 20 = 4

Let do this the way you did it to see where you may have gone wrong.

6(2x -y) = 6(13)
12x - 6y = 78
and
-2(6x + 4y) = -2(4)
-12x - 8y = -8
12x - 6y = 78
Adding this to previous equation,