To find the value of the discriminant for the quadratic equation \(12z^2 + 5z + 4 = 0\), we can use the formula for the discriminant \(D\) given by:
\[ D = b^2 - 4ac \]
where \(a\), \(b\), and \(c\) are the coefficients from the quadratic equation of the form \(az^2 + bz + c = 0\).
In this case, we have:
- \(a = 12\)
- \(b = 5\)
- \(c = 4\)
Now, substituting these values into the discriminant formula:
\[ D = 5^2 - 4 \cdot 12 \cdot 4 \] \[ D = 25 - 192 \] \[ D = 25 - 192 = -167 \]
Therefore, the value of the discriminant is \(-167\).
So the correct answer is:
\[ \boxed{-167} \]