We start with:

#5x+6y-12 = 0#

To isolate #y#, we begin by transferring terms that do not contain #y# to the opposite side of the equation.

First, let's subtract #5x# from both sides:

#5x color{orange}{-5x}+6y-12=0color{orange}{-5x}#

#=> 6y - 12 = -5x#

Now let's add #12# to both sides:

#6y - 12 color{orange}{+12}= -5x color{orange}{+12}#

#=> 6y = -5x+12#

Now that all the #y# terms and non #y# terms are on opposite sides, we can solve for #y#.

We just need to divide by #6# on both sides:

#6ycolor{orange}{-:6}= -5xcolor{orange}{-:6}+12color{orange}{-:6}#

#=> color{blue}{y = -5/6 x + 2}#