The discriminant tells us important information about the roots of a quadratic equation. For ax^2 + bx + c = 0, discriminant = b^2 - 4ac. In 2x^2 + 6x + 3 = 0, a = 2, b = 6, and c = 3. Substituting gives (6)^2 - 4(2)(3) = 12. Therefore, the correct answer is 12.