Given, Which of the given compounds can exhibit tautomerism?

All compounds show tautomerism.

Of many types of tauomerism possible, keto-enol tauomerism is the most commonly encountered one.

It is possible in presence of $\alpha$-C (wrt the carbonyl group), which is the conjugate C-H bond having sp³ hybridization.

Usually it is the $\alpha$-C of the carbonyl group constituting a triad system, however it could also sometimes be the $\gamma$-C, if there is a C=C present on $\alpha - \beta$ carbons, constituting a quinquad system.

Compound (I) & (II) are have tautomerism in a triad system, while (III) involves a quinquad system as shown here: