[Vuejs]-Vue 2 @click in child component

Inside PlusIconComponent, in your clickHandler method, you should emit some event to component’s parent passaing arguments, like:

clickHandler(){
   this.$emit('clicked', this.part)
}

On the other hand, in your parent you should catch this event with another handler, which has the same name emited by the child:

<PlusIconComponent :key="part" v-for="part in parts" :part="part" :gender="gender" :opened="(showPart===part)" @clicked="parentsHandler" />

Finally, you can implement what you want in the parent:

parentsHandler(part) {
   console.log('parent says: ', part)
}

That is the way child component comunicates with its parents. More information here