you can write your resources/views/livewire/yourcomponent.blade.php

<div>
    <div>
        <label for="client-select">Client:</label>
        <select id="client-select" wire:model="selectedClient" wire:change="loadEquipments">
            <option value="">Select Client</option>
            @foreach ($clients as $client)
                <option value="{{ $client->id }}">{{ $client->name }}</option>
            @endforeach
        </select>
    </div>
    <br><br>
    <div>
        <label for="equipment-select">Equipment:</label>
        <select id="equipment-select" wire:model="selectedEquipment">
            <option value="">Select Equipment</option>
            @foreach ($equipments as $equipment)
                <option value="{{ $equipment->id }}">{{ $equipment->name }}</option>
            @endforeach
        </select>
    </div>
</div>

and for your http/livewire/yourcomponentname.php code as follows:

<?php

namespace App\Livewire;

use App\Models\Client;
use Livewire\Component;
use App\Models\Equipment;

class DependentSelect extends Component
{
    public $selectedClient;
    public $selectedEquipment;


    public function render()
    {
        $clients = Client::all();
        $equipments = Equipment::where('client_id', $this->selectedClient)->get();

        return view('livewire.dependent-select', compact('clients', 'equipments'));
    }

    public function loadEquipments()
    {
        $this->selectedEquipment = null;
        $this->render();
    }
}

You can change the variable and components names as per your code and also check that your livewire js and css files are included in the layouts/app.blade.php file.

If you have any issue you can check here the repository i added to github. Repository on github

In my ever-evolving world of web development, delivering smooth and interactive user experiences has become my top priority. As a Laravel enthusiast, I have always appreciated the framework's capabilities in empowering developers like me to create feature-rich applications effortlessly. You can see how to create a dependent dropdown in laravel 10 livewire (https://techsolutionstuff.com/post/laravel-10-livewire-dependent-dropdown)