-6Y-3=3-6Y what the answer

The answer is the number that 'Y' must be in order for
the equation to be true.
That number is called the 'solution' to the equation.
Here's one way to go about finding it:

You said that                      - 6y - 3  =  3 - 6y

Add  6y  to each side:                - 3 =  3

Let's stop right here.
Is there any value of 'Y' that can make  -3 = 3 ?
I don't think so.
Your equation has NO SOLUTION.

There is NO NUMBER that you can write in place of 'y'
in your equation
                           - 6y - 3  =  3 - 6y
                                                       and have it work out to be true. 

That's OK.  There are lots of equations that have no solution.