To factor the expression \(12y + 6\) using the greatest common factor (GCF), first find the GCF of the coefficients (12 and 6).
The GCF of 12 and 6 is 6.
Now, factor out the GCF from the expression:
\[ 12y + 6 = 6(2y) + 6(1) \]
This can be written as:
\[ 12y + 6 = 6(2y + 1) \]
So, the factored form of \(12y + 6\) is:
\[ \boxed{6(2y + 1)} \]