Thank you for detailing.
My apologies as my original suggestion was not correct. In this particular case the header image was added via the
General -> Body/Header Styling -> Header Image(s) field of the template settings. This places an image(s) behind both the header and the showcase module positions. The text was then added to the showcase module position via a custom module with the following content...
<h4 style="color:#fff; text-align:right;">
Welcome to the Kaylee Joomla Template
</h4>
<h2 style="text-align:right; max-width: 400px; margin-left: auto; color: #d04b3d;">
Providing solutions for all industries
</h2>
<p style="color:#fff; max-width: 400px; text-align:right; margin-left: auto;">
Donec nec justo eget felis facilisis fermentum. Aliquam porttitor mauris sit amet orci. Aenean dignissim pellentesque felis.
</p>
It may be possible to use LayerSlideshow module as you have currently however it would require some custom CSS. For this I suggest sending temporary administration access to your Joomla installation to info@joomla51.com and we will examine this possibility further. For our reference please paste a link to this post in your email.
Ciaran