The correct answer is $\boxed{\frac{{\text{d}}}{2}}$.
The minimum spacing of vertical stiffeners is limited to $\frac{{\text{d}}}{2}$, where $d$ is the distance between flange angles. This is to ensure that the stiffeners are effective in resisting the buckling of the web. If the spacing is too large, the stiffeners will not be able to provide adequate support to the web and it will be more likely to buckle.
Option A, $\frac{{\text{d}}}{4}$, is too small. This would result in the stiffeners being too close together, which would be inefficient and could lead to problems with fabrication and erection.
Option B, $\frac{{\text{d}}}{3}$, is also too small. This would result in the stiffeners being too close together, which would be inefficient and could lead to problems with fabrication and erection.
Option C, $\frac{{\text{d}}}{2}$, is the correct answer. This is the minimum spacing that is required to ensure that the stiffeners are effective in resisting the buckling of the web.
Option D, $\frac{{2{\text{d}}}}{3}$, is too large. This would result in the stiffeners being too far apart, which would not be effective in resisting the buckling of the web.