Answer: 6(x+1)^2
Step-by-step explanation:
1. Find the GCF. Because you know the equation is 6x^2+12x+6, you can see that the coefficients, 6 and 12, are all factors of 6. To make factoring easier, factor out 6 from all the coefficients, which leaves you with 6(x^2+2x+1)
2. Factor the equation in the parentheses. If you have learned your perfect squares, then you know that x^2+2x+1 is (x+1)^2 because x^2+2x+1 = (x+1)(x+1) (you can foil that out if you want to check). Once finished with this, it leaves you with 6(x+1)^2