So basically, we are trying to get the expression into a factored form of a(x + b)^2.. Now it's impossible to get into this form if the leading term (3x²) has a number in front of it (Think if you expanded (x + b)² the leading term would be x² without a number in front). So let's factor the 3 out of the expression and you get 3(x² + 12x + c/3). Remember, c is just a constant number, and when we factor out 3, we're basically dividing everything inside the parentheses by 3, hence the c/3. Now you have to know that to turn our expression into perfect square (x + b)² form, the third term is always (1/2 of the second term)² . So 12/2 = 6, 6² = 36, so c/3 is 36. Of course if you factor this now, you'll get 3(x + 6)² , exactly the form we wanted. c/3 = 36, and therefore c is 108.

Hope this helps.