Problem creating full width drop down menu that appears when we hover over menu item (using jQuery)

Question

(None of the other questions here helped so far). I need the drop-down menu to appear when we hover over the parent menu item, and stay there as long as I am hovering over the parent menu item OR the drop-down menu itself.

In the code below, you can see two different ways I tried to deal with the drop-down menu through jQuery. There are two drop menus in my code. I am not using ul and li because I want to style it differently, so I just need to hide and show the drop menu div, but I am having trouble keeping it there when I am hovering over it instead of the small menu item.

The jQuery:

$(document).ready(function(){  
$("#hover-industries").hover(function(){
        $("#drop-industries").css("display", "flex");
        }, function(){
          $("#drop-industries").hide();
    });
});

$(document).ready(function(){   
$("#hover-services").hover(function(){
        $("#drop-services").css("display", "flex");
                }, function() { 
                    $("#drop-services").css("display", "none");
        }); 

});

The CSS:

        body{
            background-color: aqua;
        }      
        #big-top-menu{
            display: flex;
            justify-content: space-around;
            background-color: antiquewhite;
        }
        #big-top-menu h3{
            height: 100%;
        }
        #drop-industries{
            display: none;
            background-color: white;
            flex-direction: column;
        }
        #drop-services{
            display: none;
            background-color: white;
            flex-direction: column;
        }

The HTML:

<div id="menu-and-drop">
<div id="big-top-menu">
   <div id="hover-industries">
       <h3 id="industries-title"><a href="#">Industries</a></h3>
    <div id="drop-industries" class="one-drop">
        <a href="#">Automotive Industry</a>
        <a href="#">Biopharmaceuticals</a>
        <a href="#">Consumer Products</a>
        <a href="#">Education</a>
        <a href="#">Energy and Environment</a>
        <a href="#">Engineering Products <br>and Infrastructure</a>
    </div>
   </div>

   <div id="hover-services">
       <h3 id="services-title"><a href="#">Services</a></h3>
        <div id="drop-services" class="one-drop">
        <a href="#">Analytics</a>
        <a href="#">Corporate Finance</a>
        <a href="#">Customer Strategy</a>
        <a href="#">Information Technology</a>
        <a href="#">Operators</a>
        <a href="#">Performance Enhancement</a>
    </div>
   </div>
</div>

Answer 1

I see your handleOut function is missing the }

$("#hover-industries").hover(function(){
        $("#drop-industries").css("display", "flex");
        }, 
           function(){
            $("#drop-industries").hide();
          }
    });
});

Answer 2

One way to handle it is to position the drop menus absolutely, so that you don't mouse out of the big-top-menu so the dropdown doesn't disappear.

Here's your code in a snippet with a little css change of

position: absolute;
top: 50px;

on both of the dropdowns

$(document).ready(function(){  
$("#hover-industries").hover(function(){
        $("#drop-industries").css("display", "flex");
        }, function(){
          $("#drop-industries").hide();
    });
});

$(document).ready(function(){   
$("#hover-services").hover(function(){
        $("#drop-services").css("display", "flex");
                }, function() { 
                    $("#drop-services").css("display", "none");
        }); 

});

        body{
            background-color: aqua;
        }      
        #big-top-menu{
            display: flex;
            justify-content: space-around;
            background-color: antiquewhite;
        }
        #big-top-menu h3{
            height: 100%;
        }
        #drop-industries{
            display: none;
            position: absolute;
            top: 50px;
            background-color: white;
            flex-direction: column;
        }
        #drop-services{
            display: none;
            position: absolute;
            top: 50px;
            background-color: white;
            flex-direction: column;
        }

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>


<div id="menu-and-drop">
   <div id="big-top-menu">
      <div id="hover-industries">
         <h3 id="industries-title"><a href="#">Industries</a></h3>
         <div id="drop-industries" class="one-drop">
            <a href="#">Automotive Industry</a>
            <a href="#">Biopharmaceuticals</a>
            <a href="#">Consumer Products</a>
            <a href="#">Education</a>
            <a href="#">Energy and Environment</a>
            <a href="#">Engineering Products <br>and Infrastructure</a>
         </div>
      </div>

      <div id="hover-services">
         <h3 id="services-title"><a href="#">Services</a></h3>
         <div id="drop-services" class="one-drop">
            <a href="#">Analytics</a>
            <a href="#">Corporate Finance</a>
            <a href="#">Customer Strategy</a>
            <a href="#">Information Technology</a>
            <a href="#">Operators</a>
            <a href="#">Performance Enhancement</a>
         </div>
      </div>
   </div>
</div>