Wordpress get_option and update_option returned entered on the textbox field

Handling form fields is not related to WordPress and is off-topic here, BTW I’m answering this on how to use the options table. And your code you presented here is not relevant to your question.

Ok, first of all having form data into a field after submission could put you in risk of entering duplicate entries. BTW here’s how you can do that (follow the inline comments):

<?php
if( isset($_POST['x_submit']) ) {
    $data = array(
            'name'  => sanitize_text_field( $_POST['name'] ),
            'email' => sanitize_email( $_POST['email'] ),
            'comment'   => esc_textarea( $_POST['comment'] )
        );
    //entering data into options table
    update_option( 'my_option_key', $data );
}
?>

<?php
//having data from options table
$db_values = get_option( 'my_option_key' );

//setting empty values to avoid 'undefined index' warning
$name="";
$email="";
$comment="";

//if there's any data in options table, updating our variables with relevant data
if( $db_values ) {
    $name = $db_values['name'] ? $db_values['name'] : '';
    $email = $db_values['email'] ? $db_values['email'] : '';
    $comment = $db_values['comment'] ? $db_values['comment'] : '';
}
?>
<form method="post">
    <label>Name <input type="text" name="name" value="<?php echo isset($_POST['name']) ? $_POST['name'] : $name; ?>"></label><br>
    <label>Email <input type="email" name="email" value="<?php echo isset($_POST['email']) ? $_POST['email'] : $email; ?>"></label><br>
    <label>Comment <textarea name="comment" cols="30" rows="10"><?php echo isset($_POST['comment']) ? $_POST['comment'] : $comment; ?></textarea></label>
    <input type="submit" name="x_submit" value="Submit">
</form>

P.S.: NOTHING IS TESTED here, just follow the procedures and change it as it suits you. And important, do the necessary escaping and sanitizing.

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