Why
How
adverb
When you want to know what the circumstances are around you, you have to ask why. Why do things happen around you? Asking why is very important if you want to understand the world.
なぜ
The reading for this is an exception. The reading for 何 is just the first な from なに. You can remember the second part this way:
No one knows quite how or why that big zeppelin (ぜ) crashed in the 1930s. People are still asking today and no one has any answers. We have to keep asking until we get some.
何故復讐しようと思ったんですか。
Why were you trying to get revenge?