Hofmann's method to separate amines in a mixture uses the reagent:
(A) Benzenesulfonyl chloride.
(B) Diethyl Oxalate.
(C) Benzyl Isocyanide.
(D) p-toluenesulfonic acid.

Hint: We know that Hofmann Elimination Reaction Mechanism involves $E2$ elimination mechanism. The Hofmann exhaustive methylation mechanism starts with formation of the ammonium iodide salt then ammonium iodide salt reacts with silver oxide and gives silver iodide as precipitate.

Complete step by step solution:
Hofmann elimination reactions are the elimination reactions of quaternary ammonium salts producing tertiary amines and alkenes. It is also known as Hofmann exhaustive methylation and Hofmann degradation. The products of this reaction tertiary amines and alkenes are known as Hofmann products. Silver hydroxide and heat is used in the reaction to get the product.
According to Hofmann rule the less stable alkene will be the main product in Hofmann Elimination reactions or other such kinds of elimination reactions. This rule is used in the prediction of regioselectivity of elimination reactions. So, when you have a bulky leaving group in the elimination reaction, the least substituted alkene will be the main product. Deprotonation of water also takes place by silver oxide. It results in the formation of hydroxide ions. Now, this mixture is heated. This facilitates the elimination reaction and gives rise to alkene.
Hofmann's method to separate amines in a mixture uses the reagent diethyl oxalate. The mixture of the three amines is heated with diethyl oxalate. Primary amine forms solid oxamide, the secondary amine forms a liquid oxamic ester and the tertiary amine does not react at all.
Therefore, the correct answer is option B.

Note:
Remember that the primary use of Hofmann Elimination reaction is to synthesize alkenes. Physiological importance of Hofmann elimination reaction the design of skeletal muscle relaxant is superior to tubocurarine because of its less cardiac side effect.