Step 1: Concept
Mesityl oxide is an $\alpha,\beta$-unsaturated ketone formed by the aldol condensation of acetone followed by dehydration.
Step 2: Formation
$2 \times \text{Acetone} \xrightarrow{Ba(OH)_2} \text{Diacetone alcohol} \xrightarrow{\Delta, -H_2O} \text{Mesityl oxide}$.
Step 3: Structure Identification
IUPAC Name: 4-methylpent-3-en-2-one.
Structure: $(CH_3)_2C=CH-C(=O)CH_3$.
Step 4: Conclusion
Option (B) represents the correct structure.
Final Answer:(B)