How to change one tab's bgcolor in the navigation bar,Mystique theme

WordPress assigns a specific class to each tab in a menu automatically. Just check your source code to find it.

viewing your source code I can see that your home button has a li class of home

Additionally it has a li class of active when you are actually on the home page

So,

li.home {
     background-color: #000000;
      }

would change the color of the button in its inactive state (when you are on another page…the light grey)

and

li.home .active {
     background-color: #000000;
      }

will change the darker grey color of the home buttom (the color of the home button when you are on the home page.

and, sometimes css can be a pain and you need to be more specific, if so you can add .navigation to your css

.navigation .home {
background-color: #000000;
}
.navigation .home .active {
background-color: #000000;
}
`

yes, it’s css, so it would go in your style.css

Its probably not too important where you put them, but to keep related stuff together, I would add them in the navigation section