Hi,
I'm not really sure here. The problem with rewriting it the way you did
3xy +6y - 4x - 8
to
3xy - 4x + 6y - 8
is that the first term has an x and a y factor, where as the second and third terms have only an x and only a y factor, respectively. Thus, you did not really "group" them, but merely rewrote the expression. Supposing we looked at the expression the way you did:
3x(y - 4) + 6y - 8
is not correct. 3 is not a factor of four. This can easily be checked by multiplying 3x back into the first part of the expression:
3x(y-4)=3xy-12x, which is not equal to 3xy-4x.
I see two options for this problem:
One is to keep it as written:
3xy +6y - 4x - 8
We can now factor out a 3y for the first two terms (not the 3 is a factor of 6), which yields
3y(x+6)-4x-8
The other option is to rewrite it as you did:
3xy-4x+6y-8
Factorin out the x (and only the x!) from the first two terms yields
x(3y-4)+6y-8
These are the only two possibilities I see. I don't thin you can factor an entire expression because one term has xy, one has just x, one has just y, and one is a constant term.
Hope this helps,
-Daniel-