Step 1: Write the carbon skeleton of the compound.
The structure of 2,3-dichloro-4-methylpentane is:
\[
CH_3{-}CH(Cl){-}CH(Cl){-}CH(CH_3){-}CH_3
\]
Step 2: Identify asymmetric (chiral) carbon atoms.
An asymmetric carbon is a carbon atom attached to four different groups.
Step 3: Analyze each carbon atom.
Carbon-2: Attached to $CH_3$, $Cl$, $H$, and the rest of the chain → asymmetric
Carbon-3: Attached to $Cl$, $H$, and two different carbon chains → asymmetric
Carbon-4: Attached to two identical $CH_3$ groups, $H$, and one carbon chain → not asymmetric
Step 4: Conclusion.
There are two asymmetric carbon atoms in the given compound.