According to jewish law, there are four different methods of execution used by biblical courts. What are those four methods, and what four people from the bible, each commited suicide with one of each of those four types of deaths?

1-Stoning =>Samson
2-Burning with fire => Zimri
3-Death by sword =>Saul
4-Hanging from a tree.=>Ahithopel or Judas Iscariot.

Correct except for one minor detail. The fourth death is considered death by chocking, which could be either hanging, or hot lead poured down ones throat which is called chenek. The answer I was looking for was achitofel which you got. In Hebrew the other three deaths are called
1. death by sword- hereg
2. death by stoning- skila
3. death by fire- esh