How to display a value inside a post with a specified category from a category custom field? [closed]

You can use get_the_category() to get the categories assigned to a specific post and use the_field() or get_field() to display/get the value of a specific ACF field. (You can also use get_term_meta() in place of get_field())

So for example, the following will display a simple list of the categories (and I really mean plain simple), with the custom Image and Color fields next after the category name. Note that this assumes your Image field was set to return an image attachment’s ID.

$cats = get_the_category();
if ( ! empty( $cats ) ) {
    echo '<ul>';

    foreach ( $cats as $term ) {
        echo '<li>';

        echo $term->name;

        $selector="category_" . $term->term_id;

        // Display the category image.
        $att_id = get_field( 'image', $selector );
//      $att_id = get_term_meta( $term->term_id, 'image', true );
        echo wp_get_attachment_image( $att_id );

        // Display the category color.
        the_field( 'color', $selector );
//      echo get_term_meta( $term->term_id, 'color', true );

        echo '</li>';
    }

    echo '</ul>';
}