Step 1: State the overall transformation.
Hofmann bromamide degradation converts a primary amide ($RCONH_2$) into a primary amine ($RNH_2$) that has one fewer carbon atom than the starting amide.
Step 2: Step one of the mechanism.
Bromine reacts with the amide nitrogen to form an N-bromoamide ($RCONHB r$). The base ($NaOH$) then abstracts the N-H proton to form an anion $RCONB r^-$.
Step 3: Rearrangement step.
The nitrogen anion undergoes a 1,2-shift (Hofmann rearrangement): the alkyl group R migrates from the carbonyl carbon to the electron-deficient nitrogen, forming an isocyanate intermediate ($R$-$N=C=O$). The carbonyl carbon is thus transferred to a leaving position.
Step 4: Hydrolysis and final product.
Aqueous $NaOH$ immediately hydrolyses the isocyanate: $R$-$N=C=O + 2NaOH \rightarrow R$-$NH_2 + Na_2CO_3$. The overall equation is $RCONH_2 + Br_2 + 4NaOH \rightarrow R$-$NH_2 + Na_2CO_3 + 2NaBr + 2H_2O$.