The simplest way for this is to add an inline style into banner img tag.
Go in ACP to Templates & Styles >> Templates >> YOUR USED THEME >> Header Templates >> header and search for:
<a href="{$mybb->settings['bburl']}/index.php"><img src="{$theme['logo']}" alt="{$mybb->settings['bbname']}" title="{$mybb->settings['bbname']}" /></a>
replace this part with:
<a href="{$mybb->settings['bburl']}/index.php"><img src="{$theme['logo']}" alt="{$mybb->settings['bbname']}" title="{$mybb->settings['bbname']}" style="margin-left: 150px"/></a>
You can edit the number for margin-left style as you like.
Save changes and reload forum frontpage.