| 2y-3| = | 9-4y |

It would have been helpful if you had stated what you were trying to do/what you needed help with. But I am going to assume you want to find y.
| 2y-3| = | 9-4y | - add 4y to both sides
| 6y-3| = | 9 | - add 3 to both sides
| 6y| = | 12 | - divide everything by 6
|y| = |2|
y=2

If you go back and plug in 2 for y in the original equation it proves that this is correct...