Let's assume our checkboxes are blind
<input type="checkbox" onclick = "clickThis(event)" value="Yes"/>
<input type="checkbox" onclick = "clickThis(event)" value="Yes"/>
<input type="checkbox" onclick = "clickThis(event)" value="Yes"/>
<input type="checkbox" onclick = "clickThis(event)" value="Yes"/>
<input type="checkbox" onclick = "clickThis(event)" value="Yes"/>
<input type="checkbox" onclick = "clickThis(event)" value="Yes"/>
Now we need to find out which element was clicked, for this we can get the index of the element which is clicked.
const clickedIndex = [...event.target.parentElement.children].indexOf(event.target);
this line will gives you the index of clicked element which you can save in your localstorage
localStorage.setItem([...el.parentElement.children].indexOf(el), [...el.parentElement.children].indexOf(el));
and also you can check whenever your page load that which index is saved in your localstorage.
const inputs = document.querySelectorAll("input");
    console.log(inputs);
    if (localStorage.length > 0) {
      for (let key in localStorage) {
        if (!isNaN(localStorage[key]))
         inputs[localStorage[key]].checked = true;
      }
    }
hence the complete code
 <body>
    <input type = "checkbox" onclick = "clickThis(event)"/>
    <input type = "checkbox" onclick = "clickThis(event)"/>
    <input type = "checkbox" onclick = "clickThis(event)"/>
    <input type = "checkbox" onclick = "clickThis(event)"/>
    <input type = "checkbox" onclick = "clickThis(event)"/>
    <input type = "checkbox" onclick = "clickThis(event)"/>
    <input type = "checkbox" onclick = "clickThis(event)"/>
    <input type = "checkbox" onclick = "clickThis(event)"/>
  </body>
  <script>
    const inputs = document.querySelectorAll("input");
    console.log(inputs);
    if (localStorage.length > 0) {
      for (let key in localStorage) {
        if (!isNaN(localStorage[key]))
         inputs[localStorage[key]].checked = true;
      }
    }
    function clickThis(event) {
      console.log(event.target);
      const el = event.target;
      const clickedIndex = [...el.parentElement.children].indexOf(el);
      if (event.target.checked) {
      // adding click value to local storage
      localStorage.setItem([...el.parentElement.children].indexOf(el), [...el.parentElement.children].indexOf(el));
      } else {
        // deleting unchecked value from localstorage
        localStorage.removeItem([...el.parentElement.children].indexOf(el), [...el.parentElement.children].indexOf(el));
      }
    }
  </script>
#happy_coding
REPL link
https://repl.it/repls/SlateblueCorruptScale