In the quadratic equation \(3x^2 + 13x + 12 = 0\), we identify \(A\) and \(C\) from the standard form \(Ax^2 + Bx + C\).
Here, \(A = 3\) and \(C = 12\).
Now we calculate \(A \times C\):
\[ A \times C = 3 \times 12 = 36 \]
Therefore, the answer is:
36