Step-by-step Solution:

The given parabola is: \[ 4y^2 - 12x - 20y + 67 = 0. \] Rewriting it: \[ 4\left(y^2 - 5y\right) = -12x - 67. \] Complete the square on \( y \): \[ 4\left[\left(y - \frac{5}{2}\right)^2 - \frac{25}{4}\right] = -12x - 67. \] Simplifying: \[ 4\left(y - \frac{5}{2}\right)^2 = -12x - 42. \] \[ \left(y - \frac{5}{2}\right)^2 = -3\left(x + \frac{7}{2}\right). \] Let \( y - \frac{5}{2} = Y \) and \( x + \frac{7}{2} = X \), so the equation becomes: \[ Y^2 = -3X. \] This is the equation of a parabola with its focus at \( \left( -\frac{3}{4}, 0 \right) \). Thus, \[ x + \frac{7}{2} = -\frac{3}{4} \quad \Rightarrow \quad x = -\frac{17}{4}, \] and \[ y = \frac{5}{2}. \] (Note that it is clear from the first few steps that the \( y \)-coordinate of the focus will be \( \frac{5}{2} \). There is only one choice where the \( y \)-coordinate of the focus is \( \frac{5}{2} \).)