Step 1: Know what mesityl oxide is.
Mesityl oxide is $(CH_3)_2C=CH-CO-CH_3$, an alpha beta unsaturated ketone. It is the dehydration product of the aldol of acetone.
Step 2: See which starting material can give it.
Mesityl oxide needs two acetone molecules. So we look for the reaction that starts from acetone, which is option 2, $2CH_3COCH_3$.
Step 3: Do the aldol step.
One acetone gives up an alpha hydrogen to form a carbanion, which attacks the carbonyl of the second acetone. This builds diacetone alcohol, $(CH_3)_2C(OH)CH_2COCH_3$.
Step 4: Do the dehydration step.
On heating with $Ba(OH)_2$, water is removed from diacetone alcohol to form the double bond. \[ 2(CH_3)_2CO \rightarrow (CH_3)_2C=CHCOCH_3 + H_2O \]
Step 5: Rule out the rest.
Acetaldehyde gives crotonaldehyde, the formaldehyde mix and the benzaldehyde mix give other products, none of them mesityl oxide.
Step 6: Conclusion.
So the answer is the reaction of two acetone molecules with $Ba(OH)_2$ and heat. \[ \boxed{2CH_3COCH_3 \xrightarrow{Ba(OH)_2,\ \Delta}} \]