Follow below steps to display configurable product specific attribute values count on product listing page in Magento 2.

First, you need to override vendor/magento/module-catalog/Block/Product/ListProduct.php file in your existing module.

To override this file:

Create new file ‘di.xml’ at this path ->  app/code/Vender/Modulename/etc/. Add the following code in this new file:

 <?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:ObjectManager/etc/config.xsd">
<preference for="MagentoCatalogBlockProductListProduct" type="VenderModulenameBlockProductListProduct" />
</config>

Then create a new file named ‘ListProduct.php’ at app/code/Vender/Modulename/Block/Product/.

Add the following code in this new file:

<?php
namespace VenderModulenameBlockProduct;

class ListProduct extends MagentoCatalogBlockProductListProduct {

public function getProductDetailsHtml(MagentoCatalogModelProduct $product) {
       $html = '';
       $renderer = $this->getDetailsRenderer($product->getTypeId());
        if ($renderer) {
            if ($product->getTypeId() == MagentoConfigurableProductModelProductTypeConfigurable::TYPE_CODE) {
                $options = array();
                $productColor = array();
                $data = $product->getTypeInstance()->getConfigurableOptions($product);
                foreach ($data as $attr) {
                    foreach ($attr as $p) {

                        if ($p['attribute_code'] == 'color') {
                            if (!in_array($p['option_title'], $productColor)) {
                                $productColor[] = $p['option_title'];
                            }
                        }
                    }
                 }
                $html = '<p> ' . count($productColor) . ' </p>';
             }
             $renderer->setProduct($product);
             return $html . $renderer->toHtml();
         }
         return '';
     }

}

?>