index.html

<select id="tags-select" multiple>
  <option value="политика" selected>Политика</option>
  <option value="музыка" selected>Музыка</option>
  <option value="спорт">Спорт</option>
</select>

<p id="tags-text"><p>

index.js

var tagsSelect = document.getElementById('tags-select');
var tagsText = document.getElementById('tags-text');
function handleTagsChange() {
  var options = [].slice.call(tagsSelect.options);
  var selectedOptionsString = options
    .filter(function (option) {
       return option.selected;
    })
    .map(function (option) {
      return option.value;
    })
    .join(', ');
    
    tagsText.textContent = selectedOptionsString;
}

tagsSelect.addEventListener('change', handleTagsChange);