In a two ball-ended dipole magnet inverse-square lab, with pivoting magnet position $d_0 = 4.6\,\text{cm}$ and sliding magnet position $d_1 = 17.9\,\text{cm}$, what value should be plotted on the x-axis for $1/d^2$ (in SI units) where $d$ is the distance between the poles?

What the x-axis represents in this inverse-square test

You are plotting a quantity proportional to magnetic force against $1/d^2$ to test an inverse-square relationship. So for each measurement you need the separation distance $d$ between the two poles, then compute $1/d^2$.

Find the pole separation from the two position readings

The two given readings are positions along the same vertical scale, so the separation is their difference: $$d = d_1 - d_0 = 17.9\,\text{cm} - 4.6\,\text{cm} = 13.3\,\text{cm}$$ Convert to SI units: $$13.3\,\text{cm} = 13.3\times 10^{-2}\,\text{m} = 0.133\,\text{m}$$

Compute $1/d^2$ and round

Now calculate: $$\frac{1}{d^2} = \frac{1}{(0.133\,\text{m})^2} = \frac{1}{0.017689\,\text{m}^2} \approx 56.53\,\text{m}^{-2}$$ Rounded to the nearest whole number: $$\frac{1}{d^2} \approx 57\,\text{m}^{-2}$$