Step 1: Identify the reaction type.
The given reaction is:
\[ \text{CH}_3\text{CONH}_2 + \text{Br}_2 + 4\text{NaOH} \xrightarrow{\Delta} \, ? \]
This is the Hofmann bromamide reaction, where a primary amide is converted into a primary amine with one carbon less.
Step 2: Apply Hofmann bromamide mechanism.
In this reaction, the amide (CH\(_3\)CONH\(_2\)) reacts with Br\(_2\) and NaOH to form a primary amine (CH\(_3\)NH\(_2\)).
\[ \text{CH}_3\text{CONH}_2 \xrightarrow[\text{Br}_2]{\text{NaOH}, \Delta} \text{CH}_3\text{NH}_2 + \text{Na}_2\text{CO}_3 + \text{NaBr} + \text{H}_2\text{O} \]