I have seen myriads of captcha implementations. Some use php index files or use extra libraries, many don’t make it clear what code goes in which file or where in relation to form it goes.
I was wondering if I could get suggestions to creating captcha with my current scenario.
Any simple version would be good.

Form:

 <form action="action_page.php" method="post">
                    <div class="w3-row-padding" style="margin:0 -16px 8px -16px">
                        <div class="w3-half">
                            <input class="w3-input w3-border" type="text" placeholder="Name" required name="name" style="width:120px">
                        </div>
                        <div class="w3-half">
                            <input class="w3-input w3-border" type="text" placeholder="Email" required name="email" style="width:270px">
                        </div>
                    </div>
                    <input class="w3-input w3-border" type="text" placeholder="Message" required name="message" style="width:436px" style="height:200px">
                    <button class="w3-button w3-black w3-section w3-center" type="submit">SEND</button>
                </form>

file action_page :

<?php

 $errors = [];   
$errorMessage = '';

if (!empty($_POST)) {
$name = $_POST['name'];
$email = $_POST['email'];
$message = $_POST['message'];

if (empty($name)) {
   $errors[] = 'Name is empty';
}

if (empty($email)) {
   $errors[] = 'Email is empty';
} else if (!filter_var($email, FILTER_VALIDATE_EMAIL)) {
   $errors[] = 'Email is invalid';
}

if (empty($message)) {
   $errors[] = 'Message is empty';
}

if (empty($errors)) {

    $email_to="[email protected]";
    $email_subject="Mail From My Website";
    $email_message= "Name: ". $name . "rn" . "Email: ". $email . "rn" . "Message: " . 
 $message; 
    $headers = "From: Mern".
    "Reply-To: [email protected]rn'" . "X-Mailer: PHP/" . phpversion();
    mail($email_to, $email_subject, $email_message, $headers);  

    header("Location: mailsent.html");
    exit;
 }
 }

 ?>