**Explanation:**

Longitudinal waves are a type of mechanical wave that require a medium to propagate. They involve the displacement of particles in the medium in the same direction as the wave is traveling. Examples of longitudinal waves include sound waves and seismic waves.

**1. Vacuum:**
A vacuum is a space devoid of matter, including gases, liquids, and solids. Since longitudinal waves require a medium to propagate, they cannot travel through a vacuum. In a vacuum, there are no particles for the wave to interact with and transmit its energy. Therefore, longitudinal waves cannot travel through a vacuum.

**2. Solid:**
Solids are one of the mediums through which longitudinal waves can travel. In a solid, the particles are closely packed and can transmit the wave energy from one particle to another through vibrations. This allows longitudinal waves to propagate through solids.

**3. Liquid:**
Liquids are also a medium through which longitudinal waves can travel. Although the particles in liquids are not as closely packed as in solids, they can still transmit the wave energy through vibrations. This allows longitudinal waves to propagate through liquids.

**4. Gas:**
Gases are another medium through which longitudinal waves can travel. In gases, the particles are more spread out compared to solids and liquids, but they can still transmit the wave energy through vibrations. This allows longitudinal waves to propagate through gases.

**Conclusion:**
In conclusion, longitudinal waves cannot travel through a vacuum because they require a medium to propagate. However, they can travel through solids, liquids, and gases as long as there are particles present to transmit the wave energy through vibrations.