Hello @Web_Services,
Thanks for asking. 
First I suggest you to assign a class to the section that’s holding testimonial content under Customize > Class. After that we are going to write few CSS codes that will change the background color on hover. To help you get started I have recorded a screencast. Please take a look. https://cloudup.com/cOOqXSTlVNi
Here is the CSS code that you can add under X > Theme Options > CSS:
.custom-section-class .x-column:hover {
background-color: #d08c8c;
}
.custom-section-class .x-column{
min-height: 490px;
}
Please change the class name custom-section-class
as per your requirement.
Hope that helps you to get started.
Thanks.