Solution 1:
Update your code to correctly output the option values in the HTML:
<?php
$hb = ot_get_option('home-banner');
$hbh = ot_get_option('home-banner-height');
?>
<div class="home-banner" style="background: url('<?php echo $hb; ?>'); <?php echo !empty($hbh) ? 'height:' . $hbh . 'px;' : ''; ?>">
</div>
Explanation:
1. Use instead of to output PHP variables.
2. Combine the height style inline after checking if the value exists.