Step 1: Recall the definition of extensive properties.
An extensive property depends on the amount or size of the system. If you double the matter, the property doubles. We must count how many of the listed properties are extensive.
Step 2: Recall the definition of intensive properties.
An intensive property does not depend on the amount of matter. It stays the same whether the sample is large or small.
Step 3: List the properties to classify.
The list is volume, enthalpy, density, temperature, heat capacity, pressure, internal energy.
Step 4: Classify each as intensive or extensive.
Volume is extensive. Enthalpy is extensive. Density is intensive because it is mass divided by volume. Temperature is intensive. Heat capacity is extensive because it scales with the amount of substance. Pressure is intensive. Internal energy is extensive.
Step 5: Count the extensive ones.
The extensive properties are volume, enthalpy, heat capacity and internal energy, giving \[ 4 \] extensive properties.
Step 6: State the answer.
Therefore the number of extensive properties is $4$, matching the key.
\[ \boxed{4} \]