The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by the formula b^2 - 4ac. For the equation 9x^2 + 12x + 4 = 0, we substitute a = 9, b = 12, and c = 4 into the formula. This gives (12)^2 - 4(9)(4), which equals 144 - 144. The discriminant is 0.