To determine which compounds can exhibit tautomerism, we need to identify the presence of $\alpha$-hydrogens adjacent to a carbonyl group.$\\$Tautomerism typically involves keto-enol tautomerism, where a hydrogen atom moves from an $\alpha$-carbon to the oxygen of the carbonyl group, forming an enol.$\\$Let's analyze each compound:$\\$• Compound (I):$\\$The structure has a carbonyl group and two methyl groups attached to the $\alpha$-carbon.$\\$There are no $\alpha$-hydrogens available for tautomerism.$\\$• Compound (II):$\\$The structure has a carbonyl group and one methyl group attached to the $\alpha$-carbon.$\\$There is one $\alpha$-hydrogen available, allowing for tautomerism.$\\$• Compound (III):$\\$The structure has a carbonyl group and one methyl group attached to the $\alpha$-carbon.$\\$There is one $\alpha$-hydrogen available, allowing for tautomerism.$\\$Based on the analysis, compounds (II) and (III) can exhibit tautomerism.$\\$Therefore, the correct option is $$II and III.$\\$This corresponds to Option 4.