Magnetic moment, $\mu=\sqrt{n(n+2)}$

Where, $n=$ number of unpaired electrons

The electronic configuration for the given ions is as follow:

For $M n^{2+}[Z=25]=1 s^{2}, 2 s^{2}, 2 p^{6}, 3 s^{2} 3 p^{6}, 3 d^{2} 4 s^{0}$

$\mathop {\boxed \uparrow \boxed \uparrow \boxed \uparrow \boxed \uparrow \boxed \uparrow }\limits^{3{d^2}} $

$\mu=\sqrt{5(5+2)}=\sqrt{35}$

For $C r^{2+}[Z=24]=1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6}, 3 d^{4}, 4 s^{0}$

$\mathop {\boxed \uparrow \boxed \uparrow \boxed \uparrow \boxed \uparrow }\limits^{3{d^4}} $

$\mu=\sqrt{4(4+2)}=\sqrt{24}$

For $T i^{2+}[Z=22]=1 s^{2}, 2 s^{2} 2 p^{6}, 3 s^{2} 3 p^{6}, 3 d^{2}, 4 s^{0}$

$\mathop {\boxed \uparrow \boxed \uparrow \boxed \uparrow }\limits^{3{d^2}} $

$\mu=\sqrt{2(2+2)}=\sqrt{8}$

$\therefore$ correct order of spin only magnetic moment is

$M n^{2}+C r^{2+}>T i^{2+}$