Which type of sentence is this?
Kathleen is a competitive horseback rider, and she will be competing in the next World Equestrian Games, which are held every four years.

 - simple
 - compound-complex
 - compound
 - complex
The sentence is compound-complex. It is made up of two independent clauses and a dependent clause. The dependent clause begins with the relative pronoun which.
Kathleen is a competitive horseback rider, and she will be competing in the next World Equestrian Games, which are held every four years.