Which out of the following show Hoffmann Bromamide Degradation reaction?

\(ArCONH_2\)

The correct answer is option 3. \(ArCONH_2\).

The Hofmann bromamide degradation reaction is a chemical reaction that involves the degradation of a primary amide to an amine by treatment with bromine and a base. The reaction can be represented as follows:
The mechanism of the reaction is as follows:

Among the given options:

1. \(ArNO_2\) - This is not an amide, so it doesn't undergo the Hofmann bromamide degradation.

2. \(ArCH_2NH_2\) - This is a primary amine, not an amide. The Hofmann bromamide degradation involves the degradation of amides, not amines.

3. \(ArCONH_2\) - This is a primary amide, and it will undergo the Hofmann bromamide degradation.

4. \(ArNH_2\) - This is a primary amine, not an amide. It doesn't undergo the Hofmann bromamide degradation.

Therefore, the compound that shows the Hoffmann Bromamide Degradation reaction is option 3: \(ArCONH_2\).