Set a:hover based on class

Try this:

.menu a.main-nav-item:hover { }

In order to understand how this works it is important to read this the way the browser does. The a defines the element, the .main-nav-item qualifies the element to only those which have that class, and finally the psuedo-class :hover is applied to the qualified expression that comes before.

Basically it boils down to this:

Apply this hover rule to all anchor elements with the class main-nav-item that are a descendant child of any element with the class menu.

Cascading is biting you. Try this:

.menu > .main-nav-item:hover
    {
        color:#DDD;
    }

This code says to grab all the links that have a class of main-nav-item AND are children of the class menu, and apply the color #DDD when they are hovered.

Set a:hover based on class you can simply try:

a.main-nav-item:hover { }