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Explanation: The structure of Nitromethane is CH₃NO₂ and structure of dimethylamine (CH₃NHCH₃), as dimethylamine is a secondary amine so to obtain this, we need methyl isocyanide (CH₃NC) which we can get from methanamine through carbylamine reaction.

Step 1: Convert nitromethane to methanamine

Nitromethane (CH₃NO₂) undergoes reduction in the presence of Sn and HCl to form methanamine (CH₃NH₂)

Step 2: Convert methanamine to methyl isocyanide by Carbylamine reaction

Methanamine (CH₃NH₂) is heated with alcoholic potassium hydroxide and chloroform, the methyl isocyanide (CH₃NC) is formed.

Note: Carbylamine reaction is given only by primary amines

Primary amines when heated with chloroform and alcoholic potassium hydroxide give isocynaides (carbylamines) having very unpleasant smell, which can be easily detected.

Step 3: Convert methyl isocyanide to diethylamine

Methyl isocyanide (CH₃NC) undergoes reduction in the presence of sodium and ethyl alcohol to form diethylamine (CH₃NHCH₃-final product)