CSS can not select a parent div only when a specific child or descendent element is hovered.  You'll need some JavaScript to achieve what you seem to want.

JavaScript can be added to add something like a "hovered" class to your parent element when various mouse or touch events happen on the child div.  You could edit the CSS properties directly in JavaScript but I would use a CSS class just to keep more of the CSS concerns separate.



The :hover is closely related to your question but it doesn't solve your requirements.  :hover lets you select elements that are hovered over.  If the child is hovered, the parent is also hovered.  There is a problem though.
Here is an example of the problem with :hover:
HTML:

   OK
   Cancel


CSS:
.my-parent:hover {
   background-color: green;
}
Say you want the background of my-parent to go red when hovering over "OK".  The above example will do that.  The problem is it'll go green when hovering over the Cancel button too.