Подменю раскрывающегося меню появляются при наведении курсора на другое раскрывающееся меню.

.cat_electronics, .cat_home_appliances {
  display: inline-block;
  padding: 1rem;
}

.elect-container, .home1 {
  display: none;
  position: absolute;
}

.cat_electronics:hover > .elect-container {
  display: block;
}

.cat_home_appliances:hover > .home1 {
  display: block;
}

<div class="header_wrapper">
  <a href="index.php"><img src="images/1.jpg"></a>
</div>

<div class="search">
  <form method="get" action="search.php">
    <input type="text" name="search" placeholder="Search...">
    <button type="submit">Submit</button>
  </form>
</div>

<div class="account">
  <a href="signup.php">SignUp</a>
  <a href="signin.php">SignIn</a>
  <a href="my_account.php">My Account</a>
  <a href="cart.php">Cart</a>
  <a href="track_order.php">Track Order</a>
</div>

<div class="cat_electronics">
  <button>Elecronics</button>
    <div class="elect-container">
      <div class="elec">
        <a>Mobiles<i class="fas fa-caret-down"></i></a>
        <a>Mi</a>
        <a>Realme</a>
        <a>Samsung</a>
        <a>Sony</a>
        <a>Infinix</a>
        <a>Oppo</a>
        <a>Vivo</a>
        <a>Nokia</a>
        <a>Motorola</a>
        <a>Apple</a>
        <a>Lenovo</a>
        <a>honor</a>
        <a>Asus</a>
        <a>Google Pixel</a>
      </div>

      <div class="elec1">
        <a>Mobile Accessories<i class="fas fa-caret-down"></i></a>
        <a>Mobile Cases</a>
        <a>Headphones & Headsets</a>
        <a>Power Banks</a>
        <a>Screenguards</a>
        <a>Memory Cards</a>
        <a>Memory Cards</a>
        <a>Memory Cards</a>
        <a>Smart Headphones</a>
        <a>Mobile Cables</a>
        <a>Mobile Chargers</a>
        <a>Mobile Holders</a>
      </div>

      <div class="elec2">
        <a>Laptops<i class="fas fa-caret-down"></i></a>
        <a>Gaming Laptops</a>
        <a>Office-Work Laptops</a>
        <a>Mid-Range Laptops</a>
      </div>

      <div class="elec3">
        <a>Desktop PCs<i class="fas fa-caret-down"></i></a>
        <a>Gaming PCs</a>
        <a>Office PCs</a>
        <a>Workstation PCs</a>
        <a>Budget PCs</a>
      </div>
    </div>
</div>

<div class="cat_home_appliances">
  <button>Home Appliances</button>
    <div class="home1">
      <a>one</a>
      <a>two</a>
      <a>three</a>
  </div>
</div>