<form action="">
  <label>
    <input type="checkbox" name="question" id="other" value="other" onchange="toggle()">その他
  </label>
  <label id="other_text"  hidden>
    <input type="text" name="question" id="other_text" value="">
  </label>
</from>

function toggle() {
  var radio = document.getElementById("other");
  var text = document.getElementById("other_text");
  if (radio.checked) {
    text.removeAttribute("hidden");
  } else {
    text.setAttribute("hidden", "hidden");
  }
}