You can update any individual record in lwc using ui api i.e without writing any piece of apex logic. All you need to do it to import uiRecordApi class as shown below-
import { updateRecord } from 'lightning/uiRecordApi';
then call this method as shown below in your js handler (save method which you want to call from save button) –
const fields = {};
fields['Id'] = recordId; //populate it with current record Id
fields['Target_Areas__c'] = this.selectedTargetareaString; //populate any fields which you want to update like this
const recordInput = { fields };
updateRecord(recordInput) .then(() => {
this.dispatchEvent(
new ShowToastEvent({
title: 'Success',
message: 'Record updated',
variant: 'success'
})
);
}) .catch(error => {
this.dispatchEvent(
new ShowToastEvent({
title: 'Error creating record',
message: error.body.message,
variant: 'error'
})
);
});