Cares
Worries, Troubles
noun
The actions and things you have to 心配 about are your cares and worries.
The reading is the reading of 心配 (which you've hopefully gotten down okay by now) and 事 using the (こと) reading. It is rendaku'd, as well, so beware of the ごと (just another 心配事, ammiright?).
心配事がない
to have nothing to worry about
心配事がある
to have worries
心配事がなくなる
to have troubles disappear
心配事をわらいとばしてくれてありがとう。
Thank you for laughing my cares away.
なんだか心配事があるみたいだよ。
Apparently he's got some worries.
私の一番の心配事は、町に降り落ちる火山灰です。
My biggest worry is volcanic ash falling over the city.