Step 1: Rule out the competing reaction first.
Aldehydes that have at least one alpha hydrogen next to the carbonyl carbon undergo aldol condensation under base. Aldehydes with no alpha hydrogen, such as formaldehyde or benzaldehyde, instead undergo the Cannizzaro reaction. Since this reaction proceeds to give an addition type product here, the aldehyde in question must have an alpha hydrogen available.
Step 2: State the role of $Ba(OH)_2$.
$Ba(OH)_2$ is a mild base. It does not attack the carbonyl carbon directly; instead, it pulls off an acidic alpha hydrogen to generate a resonance stabilized enolate ion.
Step 3: Follow the enolate's attack.
This enolate is nucleophilic at the alpha carbon, and it attacks the electrophilic carbonyl carbon of a second, unreacted aldehyde molecule. This carbon to carbon bond formation is the key step of the aldol reaction.
Step 4: Identify the immediate product of that attack.
After the new carbon-carbon bond forms and the alkoxide picks up a proton, the result is a molecule that carries both a hydroxyl group and an aldehyde group, a beta-hydroxy aldehyde.
Step 5: Decide whether dehydration also happens.
Aldol product converts to the unsaturated, conjugated compound only with stronger heating or added acid to drive off water. Under the mild conditions described, the reaction is expected to stop at the addition stage.
