JSFiddle - React, Tailwind, and code Playground
HTML
<button type="button" id="mybutton"><i class="icon icon-heart"></i> 1</button>
<div id="likebox2" class="likebox" style="display: none;">
<div class="likebox-header">1 пользователю это понравилось</div>
<a href="http://localhost/2" style="float: left; padding: 5px; cursor: pointer;" title="@jamesbraga">
<img alt="image" src="http://designbump.com/wp-content/uploads/2014/01/best-free-flat-icons-001.jpg" height="32px" width="32px" />
</a>
</div>
JavaScript
$('#mybutton').on('mouseenter', function(){
$('#likebox2').show()
}).on('mouseleave', function(){
var hideTimer = setTimeout(function(){
$('#likebox2').hide()
}, 700)
$('#likebox2').on('mouseenter', function(){
clearInterval(hideTimer)
}).on('mouseleave', function(){
$(this).hide()
})
})