JSFiddle - React, Tailwind, and code Playground

HTML

<p id="billing_gorod_field">
    billing_gorod
    <input type="text" class="input-text" name="billing_gorod" id="billing_gorod">
</p>
<p id="billing_index_field">
    billing_index
    <input type="text" class="input-text " name="billing_index" id="billing_index">
</p>

<div id="order_review">
    <ul>
        <li>
            <input type="radio" id="shipping_method_1" name="shipping_method" class="shipping_method" checked="checked">
        </li>
       <li>
            <input type="radio" id="shipping_method_2" name="shipping_method" class="shipping_method">
        </li>
        <li>
            <input type="radio" id="shipping_method_0_flat_rate-16" name="shipping_method" value="flat_rate:16" class="shipping_method">
        </li>
    </ul>
</div>

CSS

#billing_index_field,
#billing_gorod_field{
    display: none;
}

JavaScript

jQuery(document).ready(function($) {
   $('input[type="radio"]').click(function() {
       if($(this).attr('value') == 'flat_rate:16') {
            $('#billing_index_field').show();   
            $('#billing_gorod_field').show();
       }

       else {
            $('#billing_index_field').hide();   
            $('#billing_gorod_field').hide(); 
       }
   });
});