JSFiddle - React, Tailwind, and code Playground

HTML

<form action="" method="" accept-charset="utf-8">
	<input type="checkbox" name="option1" value="1">
	<input type="checkbox" name="option2" value="2">
	<input type="checkbox" name="option3" value="3">
	<input type="checkbox" name="option4" value="4">
	<input type="text">
	<input type="submit" value="Отправить">
</form>

JavaScript

var GetValue = (function() {
  function GetValue() {
    this.init();
    this.events();
  }

  GetValue.prototype.init = function() {
  	this.form = document.querySelector('form');
  	this.textInput = this.form.querySelector('input[type="text"]');
  	this.checkboxes = [].slice.call(this.form.querySelectorAll('input[type="checkbox"]'));
  	this.arraySelected = new Array();
  };

  GetValue.prototype.events = function() {
  	return this.checkboxes.forEach((function(_this) {
  	  return function(el) {
	      return el.addEventListener('click', function() {
	        return _this.set(el);
	      });
  	  };
  	})(this));
  };

  GetValue.prototype.set = function (el) {
  	if (this.arraySelected.indexOf(el.value) >= 0) {
  		this.arraySelected.splice(this.arraySelected.indexOf(el.value), 1);
  		this.textInput.value = this.arraySelected;
  	} else {
  		this.arraySelected.push(el.value)
  		this.textInput.value = this.arraySelected;
  	}
  };

  return GetValue;

})();

new GetValue();