Cart item price calculation, based on chosen "days" custom field in Woocommerce

The code in your question make errors due to code formatting, surely when you copy paste it.
For example - > need to be -> or $product_price. = need to be $product_price .=…
To understand, see about PHP operators.

Here below you will find the correct way for your calculations based on rental "Period" (days):

// HERE your rental days settingsfunction get_rental_days_options() {    return array(        '2' => __("2 Days", "woocommerce"),        '4' => __("4 Days", "woocommerce"),    );}// Add a custom field before single add to cartadd_action('woocommerce_before_add_to_cart_button', 'display_single_product_custom_fields', 5);function display_single_product_custom_fields() {    // Get the rental days data options    $options = array(''  => __("Choosen period", "woocommerce")) + get_rental_days_options();    echo '<div class="custom-text text">    <h3>'.__("Rental", "woocommerce").'</h3>    <label>'.__("Start Date", "woocommerce").': </label>    <input type="date" name="rental_date" value="" class="rental_date" />    <label>Period:</label>    <select class="rental-days" id="rental-days" name="rental_days">';    foreach( $options as $key => $option ){        echo '<option value="'.$key.'">'.$option.'</option>';    }    echo '</select>    </div>';}// Get custom field value, calculate new item price, save it as custom cart item dataadd_filter('woocommerce_add_cart_item_data', 'add_custom_field_data', 20, 3);function add_custom_field_data($cart_item_data, $product_id, $variation_id) {    // HERE set the percentage rate to be applied to get the new price    $percentage  = 2;    if (isset($_POST['rental_date']) && !empty($_POST['rental_date'])) {        $cart_item_data['custom_data']['start_date'] = $_POST['rental_date'];    }    if (isset($_POST['rental_days']) && !empty($_POST['rental_days'])) {        $cart_item_data['custom_data']['rental_days'] = esc_attr($_POST['rental_days']);        $_product_id = $variation_id > 0 ? $variation_id : $product_id;        $product     = wc_get_product($_product_id); // The WC_Product Object        $base_price  = (float) $product->get_regular_price(); // Get the product regular price        $price_rate  = $cart_item_data['custom_data']['rental_days'] * $percentage / 100;        $cart_item_data['custom_data']['base_price']  = $base_price;        $cart_item_data['custom_data']['new_price']   = $base_price * $price_rate;    }    // Make each cart item unique    if (isset($cart_item_data['custom_data']['rental_days']) || isset($cart_item_data['custom_data']['start_date'])) {        $cart_item_data['custom_data']['unique_key'] = md5(microtime().rand());    }    return $cart_item_data;}// Set the new calculated cart item priceadd_action('woocommerce_before_calculate_totals', 'extra_price_add_custom_price', 20, 1);function extra_price_add_custom_price($cart) {    if ( is_admin() && ! defined( 'DOING_AJAX' ) )        return;    if ( did_action( 'woocommerce_before_calculate_totals' ) >= 2 )        return;    foreach($cart->get_cart() as $cart_item) {        if (isset($cart_item['custom_data']['new_price']))            $cart_item['data']->set_price((float) $cart_item['custom_data']['new_price']);    }}// Display cart item custom price detailsadd_filter('woocommerce_cart_item_price', 'display_cart_items_custom_price_details', 20, 3);function display_cart_items_custom_price_details($product_price, $cart_item, $cart_item_key) {    if (isset($cart_item['custom_data']['base_price'])) {        $product = $cart_item['data'];        $base_price = $cart_item['custom_data']['base_price'];        $product_price = wc_price(wc_get_price_to_display($product, array('price' => $base_price))). '<br>';        if (isset($cart_item['custom_data']['rental_days'])) {            $rental_days    = get_rental_days_options();            $product_price .= $rental_days[$cart_item['custom_data']['rental_days']];        }    }    return $product_price;}// Display in cart item the selected dateadd_filter('woocommerce_get_item_data', 'display_custom_item_data', 10, 2);function display_custom_item_data($cart_item_data, $cart_item) {    if (isset($cart_item['custom_data']['start_date'])) {        $cart_item_data[] = array(            'name'  => __("Rental start date", "woocommerce"),            'value' => date('d.m.Y', strtotime($cart_item['custom_data']['start_date'])),        );    }    if (isset($cart_item['custom_data']['rental_days'])) {        $rental_days    = get_rental_days_options();        $cart_item_data[] = array(            'name'  => __("Rental period", "woocommerce"),            'value' => $rental_days[$cart_item['custom_data']['rental_days']],        );    }    return $cart_item_data;}// Save and display custom field in orders and email notifications (everywhere)add_action( 'woocommerce_checkout_create_order_line_item', 'custom_fields_update_order_item_meta', 20, 4 );function custom_fields_update_order_item_meta( $item, $cart_item_key, $values, $order ) {    if ( isset( $values['custom_data']['date'] ) ){        $date = date( 'd.m.Y', strtotime( $values['custom_data']['date'] ) );        $item->update_meta_data( __( 'Start date', 'woocommerce' ), $date );    }    if ( isset( $values['custom_data']['rental_days'] ) ){        $rental_days = get_rental_days_options();        $item->update_meta_data( __( 'Rental period', 'woocommerce' ), $rental_days[$values['custom_data']['rental_days']] );    }}

Code goes in function.php file of your active child theme (or active theme). Tested and works.