The magnetic moment of an atom or ion with unpaired electrons is given by the formula $$\mu = \sqrt{n(n+2)}$$ Bohr magnetons (BM), where $$n$$ is the number of unpaired electrons. The magnetic moment depends on the number of unpaired electrons: more unpaired electrons lead to a higher magnetic moment.

Looking at the given options with respect to their electron configurations and calculating their respective magnetic moments based on their unpaired electrons:

• $$[\mathrm{Ar}] 3 \mathrm{~d}^7$$ has 3 unpaired electrons, yielding a magnetic moment of $$\sqrt{15}$$ BM.
• $$[\mathrm{Ar}] 3 \mathrm{~d}^8$$ has 2 unpaired electrons, for a magnetic moment of $$\sqrt{8}$$ BM.
• $$[\mathrm{Ar}] 3 \mathrm{~d}^3$$ also has 3 unpaired electrons, similar to $$3 \mathrm{~d}^7$$, so its magnetic moment is likewise $$\sqrt{15}$$ BM.
• Finally, $$[\mathrm{Ar}] 3 \mathrm{~d}^6$$ has 4 unpaired electrons, resulting in the highest magnetic moment among the options, $$\sqrt{24}$$ BM.

Hence, the electron configuration associated with the highest magnetic moment is $$[\mathrm{Ar}] 3 \mathrm{~d}^6$$.