Hi @robertrhu
Thanks for reaching out to us.
As opposed to using a checkbox, I would recommend using a true/false field. This will return true if selected and thus you can display the selected sub_field.
If you would like to make use of the display none, you may do it as follows
<?php
$selected = get_sub_field('field_name','option');
$html = "<div "
if(!$selected)
$html.='style = "display:none;"';
$html.=">My FAQ content here </div>";
?>
Hope this helps.