As alexpods says, there is no dedicated way to do this in ES6. However, for those interested, there is also a proposal for the bind operator which enables this sort of syntax:
function privateMethod() {
return `Hello ${this.name}`;
}
export class Animal {
constructor(name) {
this.name = name;
}
publicMethod() {
this::privateMethod();
}
}
Once again, this is just a proposal. Your mileage may vary.