The $E_{{\text{M}}^{3+}/{\text{M}}^{2+}}^{\circ }$ values for $\text{Cr, Mn, Fe}$ and $\text{Co}$ are $-0.41,+1.57,+0.77$ and $+1.97\text{V}$ respectively. For which one of these metals is the change in oxidation state from $+2$ to $+3$ easiest?

The question asks which metal is most easily oxidized from $+2$ to $+3$. This corresponds to the most negative (or least positive) oxidation potential.
The given values are reduction potentials ($E_{red}^{\circ }$).$\text{Cr}$: $E_{{\text{Cr}}^{3+}/{\text{Cr}}^{2+}}^{\circ }=-0.41\text{V}$.
The most negative reduction potential means it has the highest tendency to be oxidized. Thus, Chromium is easiest to oxidize to $+3$.