Step 1: Rule out the instruments that measure something else.
An ammeter measures current, and a galvanometer only detects the presence and rough direction of a small current, neither one is built to read potential difference directly.
Step 2: Recall what a potentiometer is really for.
A potentiometer is a precision tool mainly used to compare EMFs or measure them without drawing current, it is not the everyday instrument used to read the voltage across a resistor in a circuit.
Step 3: Recall how a voltmeter is built and connected.
A voltmeter has a very high internal resistance and is connected in parallel across the component whose voltage we want, so it draws almost no current and does not disturb the circuit while giving a direct reading.
Step 4: Pick the right instrument.
Since the goal is to read the potential difference across a resistor, the voltmeter is the instrument built exactly for that job.
\[ \boxed{\text{Voltmeter}} \]