* Four-legged mammal: Think of animals that run and race.
* Laryngitis: This hints at a change in sound.
* Riding and racing: This suggests something that moves quickly and can be ridden.
The Solution:
The homonym is "horse"
* A horse is a four-legged mammal.
* "Horse" sounds like "hoarse", which is a symptom of laryngitis.
* Horses are used for riding and racing.