How to put Adsense code near Logo

you will possibly need to edit header.php of your theme (in a child theme http://codex.wordpress.org/Child_Themes ) and add the adsense code, wrapped into a html div tag with a individual CSS class for easier formatting, for example after this line:
<?php mh_logo(); ?>

for more detailed theme specific suggestions, please post in https://wordpress.org/support/theme/mh-magazine-lite