Step 1: Recognise why direct conversion is not possible.
The carbylamine reaction (which produces isocyanides) requires a primary amine, not a nitro compound. So $CH_3NO_2$ must first be converted to $CH_3NH_2$ before the carbylamine step.
Step 2: Reduce nitromethane to methylamine.
\[ CH_3NO_2 \xrightarrow{Sn/HCl} CH_3NH_2 \] The $-NO_2$ group is fully reduced to $-NH_2$ using $Sn$ and $HCl$ (or $H_2/Ni$). Methylamine is the required primary amine intermediate.
Step 3: Apply the carbylamine reaction to get methyl isocyanide.
Methylamine reacts with $CHCl_3$ and alcoholic $KOH$ on heating: \[ CH_3NH_2 + CHCl_3 + 3KOH \rightarrow CH_3NC + 3KCl + 3H_2O \]
\[ \boxed{CH_3NO_2 \xrightarrow{Sn/HCl} CH_3NH_2 \xrightarrow[alc.\,KOH]{CHCl_3} CH_3NC} \]