how do i solve this equation?

Multiply by -9/4

2y - 4 = -9/4 * 48 = -108

Add 4

2y = -104

Divide by 2

y = -52

-4/9(2y - 4) = 48
-4(2y - 4) = 9(48)
-4*2y + 4*4 = 432
-8y + 16 = 432
-8y = 432 - 16
-8y = 416
y = 416/-8
y = -52

Assume you mean :-
(- 4/9) (2y - 4) = 48
- 8y + 16 = 432
- 8y = 416
y = - 52

Get rid of the -4/9 by dividing both sides by it:

(-4/9(2y-4)) / (-4/9) = 48 / (-4/9)

You get:

2y -4 = -108

Add four:

2y = -104

Divide by two:

y = -52

That should be the answer :-)

Distribute the -4/9 through.

You should get -8/9y + 16/9 = 48. It may be easier now to multiply the entire equation by 9 to get:
-8y + 16 = 432
-8y = 416
y = -52

Divide Both Sides by 4, then multiply BS by 9.

then (2y - 4) 108 = -1

2y - 4 = -1/108

2y = 4 - 1/108

y = 2 - 1/216

so y = 1.995