Step 1: Understanding the Concept
Converting an amide to a primary amine with one carbon less using \(\text{Br}_2\) and KOH is called the Hofmann bromamide (degradation) reaction.
Step 2: Apply it
\(\text{CH}_3\text{CONH}_2+\text{Br}_2+4\text{KOH}\rightarrow\text{CH}_3\text{NH}_2+\text{K}_2\text{CO}_3+2\text{KBr}+2\text{H}_2\text{O}\)
Step 3: Check the other names
Gabriel phthalimide synthesis uses phthalimide and alkyl halide, while Hofmann elimination and exhaustive alkylation involve quaternary ammonium compounds.
Final Answer:
The reaction is Hofmann degradation.
\[ \boxed{\text{(D) }\text{Hofmann degradation reaction}} \]