Instead of doing it that way, learn this rule for both intercepts. They're
just alike:

1.  To find the y-intercept, substitute 0 for the other letter x, and solve for y.

Then the y-intercept is (0, what you get for y).

2.  To find the x-intercept, substitute 0 for the other letter y, and solve for x.
Then the x-intercept is (what you get for x, 0).

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To get the y-intercept,

    3x-2y = 6

Substitute 0 for x:

  3(0)-2y = 6
      -2y = 6
        y = -3

The y-intercept is (0,-3)

-------------------------------------------------

To get the x-intercept,

    3x-2y = 6

Substitute 0 for y:

  3x-2(0) = 6
       3x = 6
        x = 2

The x-intercept is (2,0)

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Edwin

If you want to re-arrange your original equation to the form y = something, then your steps and your result should be as follows


    3x - 2y = 6

    3x - 6 = 2y   (you move the "6" from right side to the left side, changing the sign;

                   and you move "2y" from the left side to the right side, changing the sign).


Next, you divide the terms in the last equation by 2, and you get


    y = .


Everything is correct, but it is different from what is written in your post.