Question

6x-2y=24 how do u solve for y

Answer 1

It's Diophantine equation. 
First, we need to found gcd(6,(-2)):
6=2*3
(-2)=(-1)*2

So, gcd(6,-2)=2
Now, the question is. Can we dived c=24, by gcd(6,-2) and in the end get integer?
Yes we can.
$\frac{24}{2} =12$
So, we can solve it.

Now is the formula:
${\displaystyle {\begin{cases}x=x_{0}+n{\frac {b}{\gcd(a,\;b)}}\\y=y_{0}-n{\frac {a}{\gcd(a,\;b)}}\end{cases}}\quad n\in \mathbb {Z} .}$

Second, we need the first pair (x0,y0) 
 if
x=0
then
$y=(-12)$

Third, we gonna use that formula:
${\displaystyle {\begin{cases}x=-n}\\y=-3(4+n)}\end{case}\quad n\in \mathbb {Z} .}$
Congratulations! We solve it.

Answer 2

6x - 2y = 24

-2y = 24 - 6x      Multiply both sides by -1

2y = 6x - 24        Divide both sides by 2

y = (6x - 24)/2

y = 6x/2 - 24/2

y = 3x - 12