The pair in which both species have the same magnetic moment (spin only value) is:

\([Cr(H_2O)_6]^{2+}, [Fe(H_2O)_6]^{2+}\)

The correct answer is option 2. \([Cr(H_2O)_6]^{2+}, [Fe(H_2O)_6]^{2+}\).

The spin-only magnetic moment of a transition metal ion is calculated using the following formula:

\(\mu = \sqrt{n(n + 2)}\)

where n is the number of unpaired electrons.

In \([Cr(H_2O)_6]^{2+}\), the chromium metal is in a +2 oxidation state with \(3d^4\) outer electronic configuration and 4 unpaired electrons. In \([Fe(H_2O)_6]^{2+}\), the iron metal is in +2. oxidation state with \(3d^6\) outer electronic configuration and 4 unpaired electrons. Since both complexes have a same number of unpaired electrons, they have the same magnetic moment.

The other pairs do not have the same number of unpaired electrons, so they will not have the same magnetic moment.