anything; everything — used to indicate that something applies without exception.
何事も努力が大切だと言われている。
People say that effort is important in everything.
彼は何事も自分でやろうとするタイプだ。
He is the kind of person who tries to do everything himself.
何事も始めが肝心だ。
The beginning is important for anything you do.
nothing / not anything — used with a negative verb to mean not at all or nothing.
その日は何事も起こらなかった。
Nothing happened that day.
彼は何事も気にしないように見えるが、実は傷つきやすい。
He seems not to care about anything, but in fact he's sensitive.
何事もないことを願っている。
I hope that nothing (bad) happens.