Question 41164
No it is not correct 

{{{(6y^2-3Y)(Y+7)}}}

The first number {{{6y^2-3y)}}} they both have 3y in common so you can factor it out

{{{6y^2-3y=(3y)(2y-1)}}}

So the GCF is
{{{(6y^2-3Y)(Y+7)=(3y)(2y-1)(y+7)}}}