Step 1: Identify the pronoun.
The word “it” is a pronoun.
A pronoun refers back to a noun already mentioned in the sentence (called its antecedent).
Step 2: Look for the nearest suitable noun.
In the sentence:
\[
\text{“Dad, can you take my coat and drop it off at the dry cleaner's?”}
\]
The noun introduced before “it” is coat.
Step 3: Check logical meaning.
You \emph{drop off} a coat at the dry cleaner’s, not Dad or the place itself.
Hence, ‘it’ refers to
\[
\boxed{\text{Coat}}
\]